Question about inner product

1. Aug 18, 2011

JamesGoh

In one of my tutorial problems, I was asked to verify if the following function
is a valid inner product

<$x,y$>= $x1x2 + y1y2$

Note, x=(x1,x2)$^{T}$ and y=(y1,y2)$^{T}$

where T means transpose of the matrix

The tutor said to us the answer is no because it fails the linearity test

Does it fail the linearity test because of the x1 and y1 terms in front of the x2 and y2 ?

2. Aug 18, 2011

antibrane

Try explicitly calculating
$$\langle x+y,z\rangle$$
and see if it really does equal
$$\langle x,z\rangle +\langle y,z\rangle$$
If it doesn't then you know it does not satisfy linearity.

3. Aug 18, 2011

zhentil

Does <x,0*y>=0*<x,y>?

4. Aug 19, 2011

HallsofIvy

Yes, it does. But that doesn't prove anything.

5. Aug 20, 2011

Landau

No it doesn't. <x,0>=x1x2.

6. Aug 21, 2011

HallsofIvy

Oh, Blast! I was interpreting the given inner product wrong!