Find the matrix give:
Eigen values are Lamba1 & lambda2 = 1, lambda3 = -2
The eigen spaces are:
E1 = span {[1 1 0],[1 1 1]}, E2 = span {[1 -1 0]}
By normalizing the vectors then computing the matrix A for each composition I obtain:
__|1/2..1/2..0| ___|1/3..1/3..1/3| ___|1/2..-1/2..0|
1*|1/2..1/2..0| +1*|1/3..1/3..1/3| -2*|-1/2..1/2..0|
__|..0....0....0| ___|1/3..1/3..1/3| ___|...0....0....0|
I obtain the matrix:
|-1/6 11/6 1/3|
|11/6 -1/6 1/3|
|1/3 1/3 1/3|
This is the incorrect matrix for the eigenvalues and lambda values given!
I suspect when I formulated the spectral decomposition from the normalized vectors I made and error and thus cascade the incorrect values throughout. Please advise.
Thanks!