EE 226 a - Summary of Lecture 27 Review : Part 1 - Preliminaries , Detection & Estimation

II. LINEAR ALGEBRA Linear Algebra is the study of linear transformations. We used the following result on how to diagonalize an Hermitian matrix: II.1. Theorem: Diagonalization of Hermitian Matrix (Notes on Linear Algebra Theorem 6) Let H ∈ Cn×n be a Hermitian matrix, i.e., such that H = H∗. The eigenvalues λ1, . . . , λn of H are real (they are not necessarily distinct); H has n orthonormal eigenvectors {u1, . . . , un} that form a basis for C. That is, ui uj = 1{i = j}. If P = [u1| . . . |un], then P ∗HP = Λ = diag(λ1, . . . , λn) and H = PΛP ∗ = n ∑