Thread: Orthogonal Matrix

I have found the eigenvalues and vectors to be and eigenvectors .

Now I need to find an orthogonal matrix such that .
D being my diagonal matrix.

I tried Gram-Schmidting my eigenspace but that didn't work. What do I need to do?

the problem lies with your eigenvectors for 3, as both are orthogonal to (-1,1,1). so apply gram-schmidt to just those 2.

for example if we take u1 = v1 = (1,1,0), then gram-schmidt gives:

u2 = v2 - [(u1.v1)/(u1.u1)]u1 = (1,0,1) - (1/2)(1,1,0) = (1/2,-1/2,1).

by construction, u2 is orthogonal to u1, and (1/2,-1/2,1).(-1,1,1) = -1/2 + -1/2 + 1 = 0.

That gives me the Diagonal matrix



If I am not mistaken, shouldn't D have entries corresponding to the eigenvalues?

normalize the eigenvectors.

Originally Posted by Deveno

normalize the eigenvectors.

Normalizing didn't help. Here is the output:

not .

re-check your matrix product with the proper matrix, because i get:



as expected.