Some of the things I've learned every day since Oct 10, 2016
5: Eigenvalues and Invertibility
October 15, 2016Posted by on
If is an matrix and are its (not necessarily distinct) eigenvalues, then the determinant of is the product of those eigenvalues. From this, it follows that is invertible if and only if each of those eigenvalues is nonzero, since a matrix is invertible if and only if its determinant is nonzero.