Elementary Linear Algebra Howard Anton Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 7

Chapter 7 Diagonalization & Quadratic Forms 7.1 Orthogonal Matrices 7.2 Orthogonal Diagonalization 7.3 Quadratic Forms 7.4 Optimization Using Quadratic Forms 7.5 Hermitian, Unitary, and Normal Matrices

Section 7.1 Orthogonal Matrices

Orthonormal Basis

Orthogonal Diagonalization

Symmetric Matrices

Schur’s Theorem

Hessenberg’s Theorem

Section 7.3 Quadratic Forms

Conic Sections

Central conics in standard position

Definite quadratic forms

Ellipse? Hyperbola? Neither?

Section 7.4 Optimization Using Quadratic Forms

Hessian Form of the second derivative test

Section 7.5 Hermitian, Unitary and Normal Matrices

Hermitian Matrices

Unitary Matrices

Unitarily Diagonalizing a Hermitian Matrix