Log-Determinant Function and PropertiesThe log-determinant function is a function from the set of symmetric matrices in ![]() The function can be expressed in terms of the (real, positive) eigenvalues of the argument matrix This function provides a measure of the volume of an ellipsoid. Precisely, the volume of the ellipsoid ![]() is given by This means that the volume of the ellipsoid is a function of the product of the eigenvalues of the matrix Proof of the concavity of the log-determinant function: We use the fact that a function is convex if and only if its restriction to a line is. |