Assuming a complex matrix $A$ with $n$ x $m$ dimension. What does mean multiplying $A$ with its conjugate transpose and divide by Frobenius norm? ($AA^H$ / $||A||_F$ ).
I'm asking that question because I noticed something about that. suppose that I have $y = hA$, where $h$ is a matrix of dimension $n$ x $m$ too. the results of $A^Hy / ||A||_F$ has always the same sign of $y$. for that I asked
Is that something special for any complex matrix $A$ ?
If you consider observing $N$ variables $M$ times each, you may stack your observation results into a $N\times M$ matrix $A$. If we can assume that the mean of each row of $A$ is zero, then $C = AA^H$ is the $N\times N$ covariance matrix, which tells you how well can every pair of variables be described by a linear relationship. Dividing the matrix by the Frobenius norm looks like an attempt at normalization. I'm not sure what that normalization achieves however