Chapter 9
Hermitian and Positive Definite Matrices
Wayne Barrett
Brigham Young University
Information on self-adjoint (i.e., Hermitian) and positive definite linear operators (usually called positive linear operators in the literature) can be found in Section 5.3. For a finite dimensional inner product space, an orthonormal basis provides a correspondence between matrix results and linear operators (see Fact 5.3.6).
9.1 Hermitian Matrices
All matrices in this section are either real or complex, unless explicitly stated otherwise.
Definitions:
A matrix A ∈ ℂn×n is Hermitian or self-adjoint if A* = A, or element-wise, āij = aji, for i, j = 1, ..., n. The set of Hermitian matrices of order n is denoted by Hn. Note that a matrix A∈ ℝn×n is Hermitian ...
Get Handbook of Linear Algebra, 2nd Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.