Hermitian and Positive Definite Matrices
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.
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 ...