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?
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.