If A and B are arbitrary real m x n matrices, then the mapping (A, B) = trace(A"B) defines an inner product in IRX", Use this inner product to find (A, B), the norms || A|| and || B||, and the angle a 4,B between A and B for 2 -2 -27 A = -1 and B= -1 -2 -3 3 (A, B) = || A|| = ||B|| = C A,B =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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4
If A and B are arbitrary real m x n matrices, then the mapping
(A, B) = trace(A"B)
defines an inner product in R™xn Use this inner product to find (A, B), the norms ||A|| and ||B||, and the angle a A.B between A and B for
2
-2
-27
A =
-1
and B=
-1
-3
3
(A, B) =
|| ||
%3D
||B|| =
C A,B =
Transcribed Image Text:If A and B are arbitrary real m x n matrices, then the mapping (A, B) = trace(A"B) defines an inner product in R™xn Use this inner product to find (A, B), the norms ||A|| and ||B||, and the angle a A.B between A and B for 2 -2 -27 A = -1 and B= -1 -3 3 (A, B) = || || %3D ||B|| = C A,B =
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