Thank you HallsofIvy. But unfortunately, the eigenvectors are not necessarily orthogonal (orthogonal only for symmetric matrices). So your idea seems not correct.
In the example I gave earlier, if you just find a basis for the orthogonal complement of V1, e.g. [0 1 0] and [0 0 1], they are...
Hello all. This is my first post here. Hope someone can help. Thank you guys in advance.
Here is the question:
I have a n-by-n matrix A, whose eigenvalues are all real, distinct. And the matrix is positive semi-definite. It has linearly independent eigenvectors V_1...V_n. Now I have known...