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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