42 lines
1.3 KiB
Factor
42 lines
1.3 KiB
Factor
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! Copyright (c) 2012 Anonymous
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math.functions math.matrices sequences ;
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IN: rosetta-code.conjugate-transpose
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! http://rosettacode.org/wiki/Conjugate_transpose
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! Suppose that a matrix M contains complex numbers. Then the
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! conjugate transpose of M is a matrix MH containing the complex
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! conjugates of the matrix transposition of M.
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! This means that row j, column i of the conjugate transpose
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! equals the complex conjugate of row i, column j of the original
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! matrix.
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! In the next list, M must also be a square matrix.
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! A Hermitian matrix equals its own conjugate transpose: MH = M.
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! A normal matrix is commutative in multiplication with its
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! conjugate transpose: MHM = MMH.
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! A unitary matrix has its inverse equal to its conjugate
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! transpose: MH = M − 1. This is true iff MHM = In and iff MMH =
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! In, where In is the identity matrix.
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! Given some matrix of complex numbers, find its conjugate
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! transpose. Also determine if it is a Hermitian matrix, normal
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! matrix, or a unitary matrix.
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: conj-t ( matrix -- conjugate-transpose )
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flip [ [ conjugate ] map ] map ;
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: hermitian-matrix? ( matrix -- ? )
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dup conj-t = ;
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: normal-matrix? ( matrix -- ? )
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dup conj-t [ m. ] [ swap m. ] 2bi = ;
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: unitary-matrix? ( matrix -- ? )
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[ dup conj-t m. ] [ length identity-matrix ] bi = ;
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