A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices

Abstract We obtain a canonical representation for block matrices. The facilitates simple computation of the determinant, matrix inverse, and other powers matrix, as well logarithm exponential. These results are particularly useful covariance correlation matrices, where evaluation Gaussian log-likelihood estimation greatly simplified. illustrate this with an empirical application using large panel daily asset returns. Moreover, paves new ways to modeling regularizing covariance/correlation test structures in estimate regressions many variables.