unitary matrix oor Nederlands
unitary matrix
en
A matrix which when multiplied by its conjugate transpose yields the identity matrix.
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unitaire matrix
en
square complex matrix U such that UV = VU = I where V is the conjugate transpose of U
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Orthogonal group Unitary group Projective unitary group Symplectic manifold, Symplectic matrix, Symplectic vector space, Symplectic representation Hamiltonian mechanics Metaplectic group Θ10 "Symplectic group", Encyclopedia of Mathematics Retrieved on 13 December 2014.
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In mathematics, the unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation of matrix multiplication.
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U and P commute, where we have the polar decomposition A = UP with a unitary matrix U and some positive semidefinite matrix P.
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In the definition of similarity, if the matrix P can be chosen to be a permutation matrix then A and B are permutation-similar; if P can be chosen to be a unitary matrix then A and B are unitarily equivalent.
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For the three lightest quarks, there is a group-theoretical representation involving the special unitary group SU(3); for their calculations, physicists use a convenient matrix representation known as the Gell-Mann matrices, which are also used for the SU(3) gauge group that forms the basis of the modern description of strong nuclear interactions, quantum chromodynamics.
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The general unitary group (also called the group of unitary similitudes) consists of all matrices A such that A∗A is a nonzero multiple of the identity matrix, and is just the product of the unitary group with the group of all positive multiples of the identity matrix. Contents 1 Properties
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