Referring to A and B in Problem 8 , show that the mapping 〈 A , B 〉 = det ( A B ) does not define a valid inner product on M 2 ( R ) . Which of the four properties of an inner product, if any, do hold? Justify your answer. A = [ a 11 a 12 a 21 a 22 ] and B = [ b 11 b 12 b 21 b 22 ]
Referring to A and B in Problem 8 , show that the mapping 〈 A , B 〉 = det ( A B ) does not define a valid inner product on M 2 ( R ) . Which of the four properties of an inner product, if any, do hold? Justify your answer. A = [ a 11 a 12 a 21 a 22 ] and B = [ b 11 b 12 b 21 b 22 ]
Solution Summary: The author explains that the property langle A,Brangle =mathrmdet(AB) is not a valid inner product.
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