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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

4 votes

Is there any relation between trace ratio and ratio trace of positive semi-definite matrices?

There is no relationship between the two, even in the simplest case where the $n\times n$ matrices $A$ and $B$ are simultaneously diagonalizable. In that case, we can write the expressions in terms o …
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  • 1,422
1 vote

Some but not all eigenvectors mutually orthogonal

I encountered this situation when I was studying a weird kind of radiative corrections in my formal analyses of relativistic quantum field theories with weak violations of Lorentz symmetry (arXiv vers …
Buzz's user avatar
  • 1,422