- #1
essie52
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Homework Statement
Consider a matrix A in R^(nxn) . In R^n for vectors x and y, define the product
<x, y> = ((Ax)^t)(Ay).
a) For which choices of A is this an inner product?
b) For which choices of A is <x, y> = x (dot) y (the dot product)?
Homework Equations
For inner products:
a. <x, y> = <y, x>
b. <x + y, z> = <xz> + <yz>
c. <cx, y> = c<x,y>
d. <x, x> is less than 0, for all nonzero x in A
The Attempt at a Solution
<x, y> = ((Ax)^T)(Ay) = Ax . Ay