"Let A be a N×N symmetric positive semi-definite matrix with N≥2. Let D be a diagonal matrix of dimension N. I would like to measure how much A "is far" from D, i.e. I am trying to find a way to quantify how A differs from a diagonal matrix. More generally, the aim is to come up with a measure that captures the overall "level of orthogonality" of A, such that if I have another positive semi-definite matrix B, with the same dimension, I can argue that A is more or less close to being orthogonal than B, which means I am interested in a relative statement. To be more explicit: I would like to quantify how A is close to being an orthogonal matrix, and how B is close to being an orthogonal matrix, not how A and B are orthogonal to each other. Any suggestion (even partial) is welcome"