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A, BE RXn Let n EN. Consider the following binary relation for A~B 3Qe R"*" : Q. A A = QB orthogonal Matrix (a) Show that ~ is an equivalence relation is A € GL(n, R) A A B BEGL(n, R) A (A-1)"- (B-')" (b) Show:

A, BE RXn Let n EN. Consider the following binary relation for A~B 3Qe R"*" : Q. A A = QB orthogonal Matrix (a) Show that ~ is an equivalence relation is A € GL(n, R) A A B BEGL(n, R) A (A-1)"- (B-')" (b) Show:

Advanced Engineering Mathematics
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, B E RXn 2. Let n EN. Consider the following binary relation for A~ B : 3Q E R"Xn: Q. A A= QB orthogonal Matrix Rxn is (a) Show that ~ is an equivalence relation A E GL(n, R) A A~B = B€ GL(n, R) A (A-1)T ~~ (B-1)T (b) Show: = Q, ~ Q2 (c) Show: 1. Q2 € Raxn, orthogonal matrices A~B Σ-Σ (d) Show: ij=1 ij=1 %3B A = (a,)ij=1, und B = there is (Note: track ATA)
Transcribed Image Text:A, B E RXn 2. Let n EN. Consider the following binary relation for A~ B : 3Q E R"Xn: Q. A A= QB orthogonal Matrix Rxn is (a) Show that ~ is an equivalence relation A E GL(n, R) A A~B = B€ GL(n, R) A (A-1)T ~~ (B-1)T (b) Show: = Q, ~ Q2 (c) Show: 1. Q2 € Raxn, orthogonal matrices A~B Σ-Σ (d) Show: ij=1 ij=1 %3B A = (a,)ij=1, und B = there is (Note: track ATA)
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