If A and B are orthogonal, is A+B also orthogonal? Can you demonstrate Algebraically using A + B = (A + B)^T etc...?
If A and B are orthogonal, is A+B also orthogonal? Can you demonstrate Algebraically using A + B = (A + B)^T etc...?
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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If A and B are orthogonal, is A+B also orthogonal?
Can you demonstrate Algebraically using A + B = (A + B)^T etc...? Thank you.
Transcribed Image Text:Expert Answer
Step 1
Orthogonal matrix : - A Real square matrix A is said to be
orthogonal if AA" = A"A = I.
Or if AT = A-, where A"
Transpose of A
(8) Now if A and B are two orthogonal matrix of same order then A
+ B may or may not be orthogonal matrix
but if A and B are two orthogonal matrix of same order then A + B
orthogonal if and only if
AB" + BA" + I = 0
Step 2
Thus, A+B may or may not be orthogonal
Transcribed Image Text:If the n x n matrices A and B are orthogonal, which of
the matrices in Exercises 5 through 11 must be orthogo-
nal as well?
5. ЗА
6. — В
7. AB
8. A+B
9. В-1
10. В -ТАВ 11. АТ
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