- #1

thatboi

- 132

- 18

I was wondering if anyone had any thoughts on the following symmetric matrix:

$$\begin{pmatrix}

0.6 & 0.2 & -0.2 & -0.6 & -1\\

0.2 & -0.2 & -0.2 & 0.2 & 1\\

-0.2 & -0.2 & 0.2 & 0.2 & -1\\

-0.6 & 0.2 & 0.2 & -0.6 & 1\\

-1 & 1 & -1 & 1 & -1

\end{pmatrix}

$$

Notably, when one solves for the eigenvalues and eigenvectors of this matrix, one finds that for the largest magnitude eigenvalues, the eigenvectors demonstrate an oscillatory behavior (the elements within the eigenvector switch between positive and negative), whereas for the smallest magnitude eigenvalue, the eigenvectors have a "nicer" behavior. This most likely has to do with the alternative +/- 1 in the matrix but I can't quite figure it out.