# Covariance matrix multiplied by eigenvector

I got this question in one of my classes and i'm really lost. So i'm given to matrices representing the mean and the covariance. The mean is m=\begin{bmatrix}10\\0\end{bmatrix} and the covariance is cov=\begin{bmatrix}16&-12\\-12&34\end{bmatrix}. Now after I do some computation, i get the eigenvector matrix eig=\begin{bmatrix}2&-1\\1&2\end{bmatrix}

Now i'm to compute the transformation matrix trs=eigt *cov *eig. which gives \begin{bmatrix}50&0\\0&200\end{bmatrix}. Now i'm asked to explain what happened to the covariance matrix after it was transformed and why.

• The trace of a matrix is invariant under similarity transformations. The trace of the original matrix is equal to $50$, but the trace of the transformed matrix is $250$, so you’ve made an error somewhere along the way. Since your formula has a matrix transpose instead of an inverse, it looks like the eigenvector matrix is meant to be orthogonal. – amd Dec 14 '17 at 8:18