Question

Let \[M _{2X2}\] be the vector space of 2X2 matricies. Let \[M _{2X2}\] have the inner product =tr(XY ^{T}), where tr(A) denotes the trace of the matrix A. Find the diagonal 2X2 matrix closest to \[\left[\begin{matrix}-3 & 1\\ 1 & -5\end{matrix}\right]\]

Answer 1

linear algebra?

Answer 2

I get \[\left[\begin{matrix}-2 & 0 \\ 0 & -5\end{matrix}\right]\]