2
$\begingroup$

Suppose that there are $1 \times n$ vectors $x$ and $z$, $n \times n$ matrices $A$ and $B$, $n \times 1$ vector $y$.

If these are to satisfy $xABy=zBy$, what would be the relationship between these matrices and vectors?

  • 1
    In the case everything is real (and, *mutatis mutandis*, in the case everything is complex) $xABy = zBy$ if and only if $(z - xA)By = 0$, if and only if $z^T - A^T x^T \in y^\perp$, so user1551's observation is really all there is to say.2013-01-01

0 Answers 0