A Short Excursion into Matrix Algebra

Abstract

This chapter serves as a reminder of basic concepts of matrix algebra, which are particularly useful in multivariate analysis. It also introduces the notations used in this book for vectors and matrices. Eigenvalues and eigenvectors play an important role in multivariate techniques. In Sect. 2.2 and 2.3, we present the spectral decomposition of matrices and consider the maximization (minimization) of quadratic forms given some constraints.