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where $A^T$ denotes the transpose of the matrix $A$ and $\overline{A}$ denotes the conjugate matrix. | where $A^T$ denotes the transpose of the matrix $A$ and $\overline{A}$ denotes the conjugate matrix. | ||
|cite=Weisstein, Eric W. "Conjugate Transpose." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ConjugateTranspose.html | |cite=Weisstein, Eric W. "Conjugate Transpose." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ConjugateTranspose.html | ||
| − | |napomena=In all common spaces (i.e., separable Hilbert spaces), the conjugate and transpose operations commute, so | + | |napomena=In all common spaces (i.e., separable Hilbert spaces), the conjugate and transpose operations commute, so $A^H=\overline{A}^T=\overline{A^T}$ |
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The conjugate transpose is also known as the adjoint matrix, adjugate matrix, Hermitian adjoint, or Hermitian transpose. | The conjugate transpose is also known as the adjoint matrix, adjugate matrix, Hermitian adjoint, or Hermitian transpose. | ||
|see_also=Adjoint, Complex Conjugate, Conjugate Matrix, Dagger, Hermitian Matrix, Schur Decomposition, Self-Adjoint Matrix, Transpose}} | |see_also=Adjoint, Complex Conjugate, Conjugate Matrix, Dagger, Hermitian Matrix, Schur Decomposition, Self-Adjoint Matrix, Transpose}} | ||
Inačica od 09:43, 23. listopada 2014.
Definicija: nova matrica \(A^\dagger\) za zadanu matricu \(A\), čiji je element u \(i\)-tome retku i \(j\)-tome stupcu jednak kompleksno konjugiranomu elementu od \(A\) u \(j\)-tome retku i \(i\)-tome stupcu
Napomena: Definicija se odnosi na kompleksne brojeve, kada za nju možemo reći i da je hermitski konjugirana matrica. U posebnome slučaju, kada su elementi realni brojevi, pojmovi adjungirane matrice i transponirane matrice podudaraju se i u tome slučaju ne govorimo o kompleksnoj konjugaciji u definiciji jer nema učinka na realne brojeve.
Engleske istovrijednice: adjoint matrix
Struna ID: 32474
Obrađivač: Zoran Škoda
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WMW naziv: conjugate transpose
WMW klasifikacija: Algebra > Linear Algebra > Matrices > Matrix Types >
WMW definicija: The conjugate transpose of an \(m\times n\) matrix \(A\) is the \(n\times m\) matrix defined by \(A^H=\overline{A}^T\), where \(A^T\) denotes the transpose of the matrix \(A\) and \(\overline{A}\) denotes the conjugate matrix.
WMW napomena: In all common spaces (i.e., separable Hilbert spaces), the conjugate and transpose operations commute, so \(A^H=\overline{A}^T=\overline{A^T}\) The conjugate transpose is also known as the adjoint matrix, adjugate matrix, Hermitian adjoint, or Hermitian transpose.
WMW See also: Adjoint, Complex Conjugate, Conjugate Matrix, Dagger, Hermitian Matrix, Schur Decomposition, Self-Adjoint Matrix, Transpose
Izvor: Weisstein, Eric W. "Conjugate Transpose." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ConjugateTranspose.html
Struna ID: 32474