MathAction #195 Add a conjugateTranspose operation in MatrixCategory

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

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

Topics

FrontPage
- IssueTracker
  - #195 Add a conjugateTranspose operation in MatrixCategory <-- You are here.

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)