#194 tracing complex on windows ← ↑ → #196 )set functions compile on

#195 Add a conjugateTranspose operation in MatrixCategory
last edited 18 years ago

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

Editor:
Time: 2007年11月17日 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: 2005年7月28日 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}

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.

... --unknown, 2005年7月28日 11:34:17 -0500 reply

fricas

(1) -> a:=matrix ([[%i,7],[6,3*%i]])

\label{eq1}\left[ \begin{array}{cc} i & 7 \ 6 &{3 \ i} (1)

Type: Matrix(Complex(Integer))

fricas

b := map(conjugate,transpose(a)) * a

\label{eq2}\left[ \begin{array}{cc} {37}&{{11}\ i} \ -{{11}\ i}&{58} (2)

Type: Matrix(Complex(Integer))

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

fricas

determinant(b)

\label{eq3}2025 (3)

Type: Complex(Integer)