Now, using a comparison which only considers the diagonals, we would say $V(x) \le V(y)$, and, indeed, it's still true that element-by-element $V(x_k) \le V(y_k)$. What is the intuition for using definiteness to compare matrices?Īlthough the answers are nice they don't really address the intuition. ![]() But I'm struggling to get the intuition of this relationship? ![]() The idea being that if $A-B$ is pd then $B$ is smaller than $A$. ![]() In the textbook I am reading they use positive definiteness (semi-positive definiteness) to compare two covariance matrices.
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