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 $$\left[\begin{matrix}-3 & 1\ 1 & -5\end{matrix}\right]$$

Question

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

anonymous · Answer

linear algebra?

zarkon · Answer

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