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Submitted by : (unknown) at: 2007-11-17T22:06:21-08:00 (9 years ago)
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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.

axiom
a:=matrix ([[%i,7],[6,3*%i]])

\label{eq1}\left[ 
\begin{array}{cc}
i & 7 
\
6 &{3 \  i}
(1)
Type: Matrix(Complex(Integer))
axiom
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,

axiom
determinant(b)

\label{eq3}2025(3)
Type: Complex(Integer)




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