search for: ortogonal

Hello all, I have the square symetric matrix A: 2 1 1 1 2 1 1 1 2 My first question is what is the easiest way to enter this matriz in R? Second, matrix A has an eigenvalue with multiplicity 2, in this case, how could I find the two related ortogonal eigenvectors given below by R, without the help of R, I mean, I want to know how R calculate this eigenvectors related to the same eigenvalue. > evalor<-eigen(A) > evalor $values [1] 4 1 1 $vectors [,1] [,2] [,3] [1,] 0.5773503 0.8161298 0.02447130 [2,] 0.5773503...

Hi all, A good new year for everybody. Could somebody help me on a question? The Singular Value Decomposition of a matrix A gives A = U * D * t(V) I A is a M X N matrix, U is the left singular matrix (M X N), D is a diagonal singular values matrix (N X N) and V is the transpose right singular ortogonal matrix (N X N). By taking the first l columns of V, with gives a (l X l) matrix, i know that i than have a sub-space (R^L)of the original (R^M) space. I know that this sub-space basis is optimal in the least squares sense. The question is: given one 3-dim space generated by 6 vectors (A is a...