I am having an issue with a problem, but mostly because I am confused by the notation. This is the question: If Q is an n x n symmetric matrix and e1, e2 (e is epsilon) are such that 0 < e1*I </= Q </= e2*I show that 1/e2 * I </= Q^-1 </= 1/e1 *I ( </= is less or equal to) My question is how can a matrix be compared with another matrix in a quantitative manner (less than, less or equal to, greater than, etc.) I am familiar with norms or determinants being compared that way since they are a scalar, but how would n x n matricies be compared this way? Any suggestions? Also I am assuming that the epsilons are scalar multipliers. The book I am using does not do a good job of clarifying this notation, but that is all I can imagine it would be.