LaTeX and WordPress (in the wild)
Apparently, you can use LaTeX in wordpress. Alright, he is a practice problem I was working on for my exam in two weeks.
Let with where is a identity matrix and is a matrix of ones. Find the eigenvalues of .
We seek such that where is the determinant of a matrix
Now this is merely the equation for determining the eigenvalues of . Since, is idempotent the eigenvalues of must be either zero or one. In fact, since this matrix has rank one, has eigenvalues one with multiplicity one and zero with multiplicity . Therefore the eigenvalues of can be found by setting and . This yields with multiplicity and with multiplicity which are exactly the eigenvalues of .