1. Let R2,² be the vector space of 2 × 2 matrices with entries in R. a If A = then the trace of A is defined by trace(A) = a + d. C Letting AT denote the transpose of A, prove that the operation (A, B) = trace(ATB) defines an inner product on R2,2.
1. Let R2,² be the vector space of 2 × 2 matrices with entries in R. a If A = then the trace of A is defined by trace(A) = a + d. C Letting AT denote the transpose of A, prove that the operation (A, B) = trace(ATB) defines an inner product on R2,2.
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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![1. Let R2,² be the vector space of 2 × 2 matrices with entries in R.
[a b]
If A
=
'
then the trace of A is defined by trace(A) = a + d.
Letting AT denote the transpose of A, prove that the operation (A, B) = trace(ATB)
defines an inner product on R2,2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe60e14a8-856f-447c-ac90-795ae43e00b4%2F03e74ee0-414c-4b1c-8051-1d8a80fe97a3%2Fwlnumnjj_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let R2,² be the vector space of 2 × 2 matrices with entries in R.
[a b]
If A
=
'
then the trace of A is defined by trace(A) = a + d.
Letting AT denote the transpose of A, prove that the operation (A, B) = trace(ATB)
defines an inner product on R2,2
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