SOLUTION: Define the function ⟨A, B⟩ = a11b11 + a12b21 + a21b12 + a22b22 on the vector space M22. Show this function is not an inner product.

SOLUTION: Define the function ⟨A, B⟩ = a11b11 + a12b21 + a21b12 + a22b22 on the vector space M22. Show this function is not an inner product.

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Question 1167648: Define the function
⟨A, B⟩ = a11b11 + a12b21 + a21b12 + a22b22 on the vector space M22. Show this function is not an inner product.
Answer by ikleyn(52890) (Show Source): You can put this solution on YOUR website!
.


For a matrix  A = ,


the formula produces zero value (A,A),  while "true" inner product (A,A) for a non-zero A must be positive.

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