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

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


   



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(52887) About Me  (Show Source):
You can put this solution on YOUR website!
.

For a matrix  A = %28matrix%282%2C2%2C+0%2C0%2C+1%2C0%29%29,


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