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# Edit detail for #195 Add a conjugateTranspose operation in MatrixCategory revision 1 of 1

 1 Editor: Time: 2007/11/17 22:06:21 GMT-8 Note: shut up greg !!!

changed:
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It can be interesting to add a conjugateTranspose operation in MatrixCategory RectangularMatrixCategory and SquareMatrixCategory.
For example conjugateTranspose(a) * a will give a hermitian positive definite matrix.
From unknown Thu Jul 28 11:34:17 -0500 2005
From: unknown
Date: Thu, 28 Jul 2005 11:34:17 -0500
Subject:
Message-ID: <20050728113417-0500@page.axiom-developer.org>

\begin{axiom}
a:=matrix ([[%i,7],[6,3*%i]])
b := map(conjugate,transpose(a)) * a
\end{axiom}
Determinant and eigenvalues of this matrix are always real and positive.
For example,
\begin{axiom}
determinant(b)
\end{axiom}


 Submitted by : (unknown) at: 2007-11-17T22:06:21-08:00 (14 years ago) Name : Axiom Version : default friCAS-20090114 Axiom-20050901 OpenAxiom-20091012 OpenAxiom-20110220 OpenAxiom-Release-141 Category : Axiom Aldor Interface Axiom Compiler Axiom Library Axiom Interpreter Axiom Documentation Axiom User Interface building Axiom from source lisp system MathAction Doyen CD Reduce Axiom on Windows Axiom on Linux Severity : critical serious normal minor wishlist Status : open closed rejected not reproducible fix proposed fixed somewhere duplicate need more info Optional subject :   Optional comment :

It can be interesting to add a conjugateTranspose operation in MatrixCategory? RectangularMatrixCategory? and SquareMatrixCategory?. For example conjugateTranspose(a) * a will give a hermitian positive definite matrix.

axiom
a:=matrix ([[%i,7],[6,3*%i]]) (1)
Type: Matrix(Complex(Integer))
axiom
b := map(conjugate,transpose(a)) * a (2)
Type: Matrix(Complex(Integer))

Determinant and eigenvalues of this matrix are always real and positive. For example,

axiom
determinant(b) (3)
Type: Complex(Integer)