a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1. b) Consider the matrix = [a b] A = with a, b, c and d real-valued numbers. Under which condition(s) for a, b, c and d is the matrix A negative-definite?
a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1. b) Consider the matrix = [a b] A = with a, b, c and d real-valued numbers. Under which condition(s) for a, b, c and d is the matrix A negative-definite?
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.1: The Determinants Of A Matrix
Problem 18E: Find the determinant of the matrix in Exercise 16 using the method of expansion by cofactors. Use a...
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