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last edited 16 years ago |
Edit detail for #195 Add a conjugateTranspose operation in MatrixCategory revision 1 of 1
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Editor:
Time: 2007/11/17 22:06:21 GMT-8 |
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| Note: shut up greg !!! | ||
changed: - 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}
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, Thu, 28 Jul 2005 11:34:17 -0500 reply
axiom
a:=matrix ([[%i,7], [6, 3*%i]])
![\label{eq1}\left[
\begin{array}{cc}
i & 7
\
6 &{3 \ i}](images/5140784752452357107-16.0px.png "\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}](images/8489444392743464708-16.0px.png "\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)
 | (3) |
Type: Complex(Integer)