Matrix - Inner Products and Dot Products

[essie52]

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

 

[micromass]

So, what did you already try to solve the problem?

 

[essie52]

Never mind. I figured it out but thanks anyway.

 

[moonray]

whats the difference between matrix multiplication and a matrix dot product Give examples please