Talk:Conjugate transpose

Bug in Factor

Ruby and Octave give the same answer.

$M\times M^{H}={\begin{bmatrix}1+2i&0\\0&3+4i\end{bmatrix}}\times {\begin{bmatrix}1-2i&0\\0&3-4i\end{bmatrix}}={\begin{bmatrix}5&0\\0&25\end{bmatrix}}$

Factor gives a different answer.

$M\times M^{H}={\begin{bmatrix}1+2i&0\\0&3+4i\end{bmatrix}}\times {\begin{bmatrix}1-2i&0\\0&3-4i\end{bmatrix}}={\begin{bmatrix}-3-4i&0\\0&-7-24i\end{bmatrix}}$

If Ruby and Octave are correct, then $M$ is a normal matrix. If Factor is correct, then $M$ is not a normal matrix. Factor is wrong. Factor's matrix multiplication has a bug: Factor confuses Hermitian inner product with scalar product, and calculates A × B in place of A × B. --Kernigh 00:30, 17 March 2012 (UTC)