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Matrix in linear algebra
especially in linear algebra and matrix theory, the commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of
Commutation_matrix
Mathematical operation on matrices
matrices, called the "commutation" matrix. The Commutation matrix Sp, q can be constructed by taking slices of the Ir identity matrix, where r = p q {\displaystyle
Kronecker_product
Mathematical concept in algebra
Matrices A {\displaystyle A} that commute with matrix B {\displaystyle B} are called the commutant of matrix B {\displaystyle B} (and vice versa). A set
Commuting_matrices
Topics referred to by the same term
in a group or ring Commutation matrix, a permutation matrix which is used for transforming the vectorized form of another matrix into the vectorized
Commute
Conversion of a matrix or a tensor to a vector
transpose is given by the commutation matrix. The vectorization is frequently used together with the Kronecker product to express matrix multiplication as a
Vectorization_(mathematics)
Matrices important in quantum mechanics and the study of spin
and δjk is the Kronecker delta. I denotes the 2 × 2 identity matrix. These anti-commutation relations make the Pauli matrices the generators of a representation
Pauli_matrices
Matrix equal to its conjugate-transpose
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose
Hermitian_matrix
Formulation of quantum mechanics
that AB − BA does not necessarily equal 0. The fundamental commutation relation of matrix mechanics, ∑ k ( X n k P k m − P n k X k m ) = i ℏ δ n m {\displaystyle
Matrix_mechanics
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries
List_of_named_matrices
Probability distribution
p 2 × p 2 {\displaystyle K_{pp}{\text{ is a }}p^{2}\times p^{2}} commutation matrix C o v ⊗ ( W − 1 , W − 1 ) = E ( W − 1 ⊗ W − 1 ) − E ( W − 1 ) ⊗ E
Inverse-Wishart_distribution
Prof Johann W. Kolar , sparse matrix converters avoid the multi step commutation procedure of the conventional matrix converter, improving system reliability
Sparse_matrix_converter
Irreducible representation of the rotation group SO
\{-{\mathcal {P}}_{i}\}} . An important property of the Wigner D-matrix follows from the commutation of R ( α , β , γ ) {\displaystyle {\mathcal {R}}(\alpha
Wigner_D-matrix
Matrix operation generalizing exponentiation of scalar numbers
{\displaystyle \mathrm {I} _{k}} is the Identity matrix of order k {\displaystyle k} . This follows from the commutation of the summands of the Kronecker sum and
Matrix_exponential
Identifies the commutant of a specific von Neumann algebra
In mathematics, a commutation theorem for traces explicitly identifies the commutant of a specific von Neumann algebra acting on a Hilbert space in the
Commutation theorem for traces
Commutation_theorem_for_traces
Four-dimensional number system
, q ] = 2 p × q , {\displaystyle [p,q]=2p\times q,} which gives the commutation relationship q p = p q − 2 p × q . {\displaystyle qp=pq-2p\times q.}
Quaternion
Data input device
Arstechnica. "Electrical commutation matrixer keyboards for computers". IOPscience.org. Community, QMK. "How a Keyboard Matrix Works". QMK Firmware. Retrieved
Computer_keyboard
Matrix representing the effect of scattering on a physical system
In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering
S-matrix
Type of mathematical equation
matrix exponential solution may be reduced to a simple form. Below, this solution is displayed in terms of Putzer's algorithm. When this commutation relation
Matrix_differential_equation
German physicist (1901–1976)
series of papers with Max Born and Pascual Jordan, during the same year, his matrix formulation of quantum mechanics was substantially elaborated. He is known
Werner_Heisenberg
Mathematical theorem
number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators. It is named after
Stone–von_Neumann_theorem
d − d a = c b − b c , (cross commutation relation) . {\displaystyle ad-da=cb-bc,~~~{\text{(cross commutation relation)}}.} Below are presented some
Manin_matrix
Device converting an AC waveform to another AC waveform
pp. 637 – 644, 1989. L. Wei, T. A. Lipo, “A Novel Matrix Converter Topology with Simple Commutation“, in Proceedings of the 36th IEEE IAS’01, Chicago
AC-to-AC_converter
Mathematical operation in quantum optics, general relativity and other areas of physics
Bogoliubov transformation is an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra. This
Bogoliubov_transformation
Generators of the Clifford algebra for relativistic quantum mechanics
matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra C l 1 , 3 ( R ) . {\displaystyle
Gamma_matrices
Property of some mathematical operations
the French adjective commutatif, which is derived from the French noun commutation and the French verb commuter, meaning "to exchange" or "to switch", a
Commutative_property
Matrix symmetric about its center
involutory matrix K (i.e., K2 = I ) or, more generally, a matrix K satisfying Km = I for an integer m > 1. The inverse problem for the commutation relation
Centrosymmetric_matrix
Formula in Lie theory
X} and Y {\displaystyle Y} . This result is behind the "exponentiated commutation relations" that enter into the Stone–von Neumann theorem. A simple proof
Baker–Campbell–Hausdorff formula
Baker–Campbell–Hausdorff_formula
Basis for the SU(3) Lie algebra
such transformations. The 8 generators of SU(3) satisfy the commutation and anti-commutation relations [ λ a , λ b ] = 2 i ∑ c f a b c λ c , { λ a , λ b
Gell-Mann_matrices
Intrinsic quantum property of particles
representation of the rotation group S O ( 3 ) {\displaystyle SO(3)} . Spin obeys commutation relations analogous to those of the orbital angular momentum: [ S ^ j
Spin_(physics)
Family of linear transformations
coordinates of a Lorentz generator with respect to this basis. Three of the commutation relations of the Lorentz generators are [ J x , J y ] = J z , [ K x
Lorentz_transformation
Foundational principle in quantum physics
In the case of position and momentum, the commutator is the canonical commutation relation [ x ^ , p ^ ] = i ℏ . {\displaystyle [{\hat {x}},{\hat {p}}]=i\hbar
Uncertainty_principle
Operators useful in quantum mechanics
{\frac {d}{dq}}q-q{\frac {d}{dq}}=1,} coinciding with the usual canonical commutation relation − i [ q , p ] = 1 {\displaystyle -i[q,p]=1} , in position space
Creation and annihilation operators
Creation_and_annihilation_operators
Quantum mechanical operator related to rotational symmetry
{L} =i\hbar \mathbf {L} } The commutation relations can be proved as a direct consequence of the canonical commutation relations [ x l , p m ] = i ℏ δ
Angular_momentum_operator
Anticommutating number
presupposed properties. Such objects, which, form an algebra under anti-commutation, are called the Grassmann algebra or Exterior algebra. Having such motivation
Grassmann_number
Technology of power electronics
its commutation problem and complex control keep it from being broadly utilized in industry. Unlike the direct matrix converters, the indirect matrix converters
Power_electronics
Concept in physics and mathematics
is spanned by H, Pi, Ci and Lij (an antisymmetric tensor), subject to commutation relations, where [ H , P i ] = 0 {\displaystyle [H,P_{i}]=0} [ P i ,
Galilean_transformation
Description of a quantum-mechanical system
systems and make predictions. Other formulations of quantum mechanics include matrix mechanics, introduced by Werner Heisenberg, and the path integral formulation
Schrödinger_equation
German–British physicist (1882–1970)
centres for physics. In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. The following year, he formulated
Max_Born
Approach to quantum theory
quantization conditions (commutation relations) for a quantum field theory. Unlike the canonical formalism, which postulates commutation relations, or the path
Schwinger's quantum action principle
Schwinger's_quantum_action_principle
Mathematical concept
{\displaystyle \omega } can be represented by a matrix. The conditions above are equivalent to this matrix being skew-symmetric, nonsingular, and hollow
Symplectic_vector_space
Group of rotations in 3 dimensions
definition of them acquires a factor of i. Likewise, commutation relations acquire a factor of i. The commutation relations for the t i {\displaystyle {\boldsymbol
3D_rotation_group
Property of operations
determinant of an idempotent matrix is either 0 or 1. If the determinant is 1, the matrix necessarily is the identity matrix. In the monoid ( E E , ∘ )
Idempotence
German physicist and politician (1902–1980)
and quantum field theory. He contributed much to the mathematical form of matrix mechanics, and developed canonical anticommutation relations for fermions
Pascual_Jordan
Type of mathematical expression
which x satisfies no other relations than the obligatory ones, plus commutation with all elements of R (that is xr = rx). To do this, one must add all
Polynomial
Mathematical description of fermions
taken as C4, and its elements will be Dirac spinors. For reference, the commutation relations of so(3,1) are with the spacetime metric η = diag(−1, 1, 1
Dirac_spinor
quantum-mechanical systems with analytical solutions. bra–ket notation canonical commutation relation complete set of commuting observables Heisenberg picture Hilbert
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
Group in group theory and physics
{\begin{pmatrix}1&a&c\\0&1&b\\0&0&1\\\end{pmatrix}}} under the operation of matrix multiplication. Elements a, b and c can be taken from any commutative ring
Heisenberg_group
Group of unitary complex matrices with determinant of 1
I_{n}+\sum _{c=1}^{n^{2}-1}{d_{abc}\,T_{c}}~.} The factor of i in the commutation relation arises from the physics convention and is not present when using
Special_unitary_group
16-element matrix group
matrices, including the identity. The single-qubit Pauli group is a 16-element matrix group, consisting of the 4 Pauli matrices each with 4 possible phase factors
Pauli_group
8-bit microcontroller family by Infineon
DC-motors using Hall sensors or back-EMF detection. Furthermore, block commutation and control mechanisms for multi-phase machines are supported. LEDTSCU
XC800_family
Properties underlying modern physics
above commutation relations are the same as for spins a and b have components given by multiplying Kronecker delta values with angular momentum matrix elements:
Symmetry_in_quantum_mechanics
Function acting on the space of physical states in physics
written in matrix form to map one basis vector to another. Since the operators are linear, the matrix is a linear transformation (aka transition matrix) between
Operator_(physics)
Mapping between functions in the quantum phase space
In what follows, we fix operators P and Q satisfying the canonical commutation relations, such as the usual position and momentum operators in the Schrödinger
Wigner–Weyl_transform
group isomorphism, which is a semidirect product of N and H, with the commutation of elements of N and H defined by φ {\displaystyle \varphi } . ≀ In group
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
1925 physics article by Werner Heisenberg
the canonical commutation relation, where the symbol Q {\displaystyle Q} is the matrix for displacement, P {\displaystyle P} is the matrix for momentum
Umdeutung_paper
Algebraic structure used in analysis
operators on the space of states that satisfy certain natural commutation relations. These commutation relations typically come from a symmetry of the problem—specifically
Lie_algebra
Pictorial representation of the behavior of subatomic particles
matters. The form of the singularity can be understood from the canonical commutation relations to be a delta-function. Defining the (Euclidean) Feynman propagator
Feynman_diagram
Formulation of quantum mechanics
probabilities of all physically possible outcomes must add up to one) of the S-matrix is obscure in the formulation. The path-integral approach has proven to
Path-integral_formulation
Clifford algebra in 4 dimensions
in 1928 in developing the Dirac equation for spin-1/2 particles with a matrix representation of the gamma matrices, which represent the generators of
Dirac_algebra
Gamma matrices for arbitrary Clifford algebras
_{a}\cdot \Gamma _{b}\cdot \Gamma _{c}\cdots {}} and note that the anti-commutation property allows us to simplify any such sequence to one in which the
Higher-dimensional gamma matrices
Higher-dimensional_gamma_matrices
Coefficients of an algebra over a field
{\displaystyle \sigma _{i}} . The generators of the group SU(2) satisfy the commutation relations (where ε a b c {\displaystyle \varepsilon ^{abc}} is the Levi-Civita
Structure_constants
\langle \beta |} . Density matrix Physically, the density matrix is a way to represent pure states and mixed states. The density matrix of pure state whose ket
Glossary of elementary quantum mechanics
Glossary_of_elementary_quantum_mechanics
Markovian master equation of a quantum system weakly coupled to its environment
master equation that describes the time evolution of the reduced density matrix ρ of a strongly coupled quantum system that is weakly coupled to an environment
Redfield_equation
Theorem for reducing high-order derivatives
3 , … , N ) {\displaystyle (i=1,2,3,\ldots ,N)} . They satisfy the commutation relations for bosonic operators [ a ^ i , a ^ j † ] = δ i j 1 ^ {\displaystyle
Wick's_theorem
Tensor operator generalizes the notion of operators which are scalars and vectors
coefficients of order δ θ {\displaystyle \delta \theta } , one can derive the commutation relation with the rotation generator: [ V ^ a , J ^ b ] = ∑ c i ℏ ε a
Tensor_operator
Formulation of the quantum many-body problem
the commutation of the boson operators. The raising and lowering operators of the quantum harmonic oscillator also satisfy the same set of commutation relations
Second_quantization
Representation theory of the symplectic group
two representations of the Weyl commutation relations. By Schur's lemma and the Gelfand–Naimark construction, the matrix coefficient of any vector determines
Oscillator_representation
MOSFET that can handle significant power levels
drain inductance, plus a feedback effect that makes commutation last longer, thus increasing commutation losses. at the beginning of a fast turn-on, due to
Power_MOSFET
Description of physical properties at the atomic and subatomic scale
{\displaystyle {\hat {P}}} do not commute, but rather satisfy the canonical commutation relation: [ X ^ , P ^ ] = i ℏ . {\displaystyle [{\hat {X}},{\hat {P}}]=i\hbar
Quantum_mechanics
Executed American murderer (1963–1992)
Pardons and Paroles held a hearing on whether Garrett should receive a commutation to life in prison but the death sentence was retained by a 17 to 1 vote
Johnny_Frank_Garrett
Representation of angular momentum tensor product states important to physics
{\hat {V}}_{+}]=0.} All other commutation relations follow from hermitian conjugation of these operators. These commutation relations can be used to construct
Clebsch–Gordan coefficients for SU(3)
Clebsch–Gordan_coefficients_for_SU(3)
Conserved physical quantity; rotational analogue of linear momentum
angles). This caveat is reflected in quantum mechanics in the non-trivial commutation relations of the different components of the angular momentum operator
Angular_momentum
Quantum field theory using noncommutative mathematics
noncommutative. One commonly studied version of such theories has the "canonical" commutation relation: [ x μ , x ν ] = i θ μ ν {\displaystyle [x^{\mu },x^{\nu }]=i\theta
Noncommutative quantum field theory
Noncommutative_quantum_field_theory
Lie group of Lorentz transformations
^{\rho }}_{\mu }-\eta ^{\mu \sigma }{\delta ^{\rho }}_{\nu }} . The commutation relations are [ M μ ν , M ρ σ ] = M μ σ η ν ρ − M ν σ η μ ρ + M ν ρ η
Lorentz_group
Locality condition in quantum field theory
condition requiring commutation relations of local operators to vanish for spacelike separations, is a sufficient condition for the S-matrix to satisfy cluster
Cluster_decomposition
Quantum mechanical model
following commutators can be easily obtained by substituting the canonical commutation relation, [ a ^ , a ^ † ] = 1 , [ N ^ , a ^ † ] = a ^ † , [ N ^ , a ^
Quantum_harmonic_oscillator
Statistical model in quantum mechanics of magnetic materials
)\\C(\lambda )&D(\lambda )\end{pmatrix}},} which satisfies fundamental commutation relations (FCRs) similar in form to the Yang–Baxter equation used to
Quantum_Heisenberg_model
Active non-reciprocal three-port device
rings of coupled resonators. Another design approach relies on staggered commutation and integrated circuit techniques. Compared to passive (ferrite) circulators
Active_circulator
Branch of mathematics
whose algebra is generated by two unitary elements satisfying a twisted commutation relation and which has served as a test case for noncommutative versions
Noncommutative_geometry
Transition rate formula
initial and final states of the system (described by the square of the matrix element of the perturbation) as well as the density of states. It is also
Fermi's_golden_rule
Angular momentum deriving from photon spin
convention has been applied. To quantize light, the basic equal-time commutation relations have to be postulated, [ A μ ( x , t ) , π ~ ν ( x ′
Spin angular momentum of light
Spin_angular_momentum_of_light
Result in enumerative combinatorics and linear algebra
Zbl 0108.25105. P. Cartier and D. Foata, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Mathematics, no. 85, Springer, Berlin
MacMahon's_master_theorem
Mathematical sequences in combinatorics
Press, ISBN 978-1-5848-8780-5 Mansour, Toufik; Schork, Mathias (2015), Commutation Relations, Normal Ordering, and Stirling Numbers, CRC Press, ISBN 978-1-4665-7989-7
Stirling_number
Formula for 3D vector rotation
shown to be equivalent to the Euler-Rodrigues equation by exploiting the commutation relationship q 2 q 1 = q 1 q 2 − 2 k 1 × k 2 {\displaystyle
Euler–Rodrigues_formula
Austrian and American bodybuilder, actor and politician (born 1947)
inform Santos' family or the San Diego County prosecutors about the commutation. They learned about it in a call from a reporter. The Santos family,
Arnold_Schwarzenegger
Four-vector analogue of the gradient operation
{k}}=-i{\vec {\nabla }}} In quantum mechanics (physics), the canonical commutation relation is the fundamental relation between canonical conjugate quantities
Four-gradient
Mathematical structures that allow quantum mechanics to be explained
commutation relations. The Stone–von Neumann theorem dictates that all irreducible representations of the finite-dimensional Heisenberg commutation relations
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Type of unphysical field in quantum field theory which provides mathematical consistency
fields. Because Grassmann numbers anti-commute, they resemble the anti-commutation property of the Pauli exclusion principle, and thus are sometimes taken
Faddeev–Popov_ghost
First case of a Lie group that is both compact and non-abelian
\qquad XX~=~~~~O,\qquad YY~=~~O,} where O is the 2×2 all-zero matrix. Hence their commutation relations are [ H , X ] = 2 X , [ H , Y ] = − 2 Y , [ X , Y
Representation theory of SU(2)
Representation_theory_of_SU(2)
Representation of the symmetry group of spacetime in special relativity
eigenvectors of J2 and J3. Compute matrix elements of J1, J2, J3 and K1, K2, K3. Enforce Lie algebra commutation relations. Require unitarity together
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Theoretical framework in physics
{a}}^{\dagger }} , respectively, where † denotes Hermitian conjugation. The commutation relation between the two is [ a ^ , a ^ † ] = 1. {\displaystyle \left[{\hat
Quantum_field_theory
Symmetry between bosons and fermions
algebra. Expressed in terms of two Weyl spinors, has the following anti-commutation relation: { Q α , Q ¯ β ˙ } = 2 ( σ μ ) α β ˙ P μ {\displaystyle \{Q_{\alpha
Supersymmetry
Generalization of the ice-type (six-vertex) models
(u)&=[\Theta (0)H(u)\Theta (u)]^{N}.\end{aligned}}} The existence and commutation relations of such a function are demonstrated by considering pair propagations
Eight-vertex_model
Concept in mathematics
that it contains a basis e , h , f {\displaystyle e,h,f} satisfying the commutation relations [ e , f ] = h {\displaystyle [e,f]=h} , [ h , f ] = − 2 f {\displaystyle
Special_linear_Lie_algebra
No-go theorem pertaining the triviality of space-time and internal symmetries
conformal algebra, which consists of the Poincaré algebra together with the commutation relations for the dilaton generator and the special conformal transformations
Coleman–Mandula_theorem
Raising and lowering operators
3,4,\dots )\\0&{\mbox{if any two labels are the same}}\end{matrix}}\right.} The commutation relations are simply carried over to infinite dimensions [
Anti-symmetric_operator
Statistics applied to risk in insurance and other financial products
techniques to make the calculations as easy as possible, for example "commutation functions" (essentially precalculated columns of summations over time
Actuarial_science
Mathematics of a particle physics model
are annihilation operators is a convention, imposed by the sign of the commutation relations postulated for them. An important step in preparation for calculating
Mathematical formulation of the Standard Model
Mathematical_formulation_of_the_Standard_Model
Integral transform
operator with the position operator and leave invariant the canonical commutation relations. Canonical transforms are used to analyze differential equations
Linear canonical transformation
Linear_canonical_transformation
Physical fields obeying the Schrödinger equation
that the matrix elements of ψ ( x ) {\textstyle \psi (x)} and ψ † ( x ) {\textstyle \psi ^{\dagger }(x)} have harmonic oscillator commutation relations
Schrödinger_field
COMMUTATION MATRIX
COMMUTATION MATRIX
Surname or Lastname
English
English : from Old Norse drengr ‘young man’, but with more than one possible interpretation. It may reflect the personal name (originally a byname) of this form, which had some currency in the most Scandinavian-influenced areas of medieval England. Alternatively it may reflect the Middle English borrowing of the vocabulary word in the sense ‘servant’, later a technical term of the feudal system of Northumbria for a free tenant who held land by military and agricultural service, sometimes paying rent as well or in commutation.
Girl/Female
British, English, German
Commutative Form of Louise; Renowned in Battle
Boy/Male
Indian, Malayalam
Commutation
Girl/Female
British, English
Commutative Form of Louise; Renowned in Battle
COMMUTATION MATRIX
COMMUTATION MATRIX
Girl/Female
Tamil
Young woman
Girl/Female
American, Australian, Latin
A Form of Rosana; Gracious
Boy/Male
Muslim
Hope, Expectation, Wish, Desire, Trust, Greed
Biblical
their change; their sleep
Boy/Male
Hindu, Indian, Marathi
Brought Together
Girl/Female
Hindi Indian
Divine Mother.
Boy/Male
Hindu, Indian
Beneficent to All
Female
English
 English variant spelling of Latin Laura, LARA means "laurel." Compare with another form of Lara.
Boy/Male
Indian
In Front of the Eyes
Boy/Male
Indian
Autum, Bright
COMMUTATION MATRIX
COMMUTATION MATRIX
COMMUTATION MATRIX
COMMUTATION MATRIX
COMMUTATION MATRIX
n.
Erroneous computation; false reckoning.
v. t.
To exceed in reckoning or computation.
n.
The act or process of computing; calculation; reckoning.
n.
The act of drinking or tippling together.
n.
Enumeration; computation.
n.
The change of a penalty or punishment by the pardoning power of the State; as, the commutation of a sentence of death to banishment or imprisonment.
n.
The act or process of confuting; refutation.
n.
See Commutator.
n.
Computation.
n.
Refutation; confutation; contradiction.
n.
Reckoning; computation.
n.
A substitution, as of a less thing for a greater, esp. a substitution of one form of payment for another, or one payment for many, or a specific sum of money for conditional payments or allowances; as, commutation of tithes; commutation of fares; commutation of copyright; commutation of rations.
n.
The act of giving one thing for another; barter; exchange.
n.
Account; reckoning; computation.
a.
Capable of being measured; susceptible of mensuration or computation.
n.
An erroneous computation.
a.
Relative to exchange; interchangeable; reciprocal.
n.
The result of computation; the amount computed.
n.
Confutation.
n.
A passing from one state to another; change; alteration; mutation.