a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1. b) Consider the symmetric matrix A .b == [a b] with a and b real-valued numbers. Under which condition(s) for a and b is the matrix A positive-definite ?
a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1. b) Consider the symmetric matrix A .b == [a b] with a and b real-valued numbers. Under which condition(s) for a and b is the matrix A positive-definite ?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1.
b) Consider the symmetric matrix
A
.b
== [a b]
with a and b real-valued numbers. Under which condition(s) for a and b is the
matrix A positive-definite ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6070c27-0824-4884-a918-195c8f609349%2F450aae7a-7553-4adc-8522-052b2646714d%2Fuhrnyr9_processed.png&w=3840&q=75)
Transcribed Image Text:a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1.
b) Consider the symmetric matrix
A
.b
== [a b]
with a and b real-valued numbers. Under which condition(s) for a and b is the
matrix A positive-definite ?
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