Re: eigenvectors and eigenvalues of a matrix

2014-01-08 Thread Tharindu Rusira
want to find eigenvalues/eigenvectors of the covariance matrix XTX. So my workaround is to find singular values and right singular vector of X in order to use the following equivalency. Comparison with the eigenvector factorisation of *X*T*X* establishes that the right singular vectors *W* of *X

Re: eigenvectors and eigenvalues of a matrix

2014-01-08 Thread Sebastian Schelter
eigenvalues/eigenvectors of the covariance matrix XTX. So my workaround is to find singular values and right singular vector of X in order to use the following equivalency. Comparison with the eigenvector factorisation of *X*T*X* establishes that the right singular vectors *W* of *X

Re: eigenvectors and eigenvalues of a matrix

2014-01-08 Thread Ted Dunning
vectors eigenMap.put(singularValues[i] * singularValues[i], (DenseVector) eigenVectors.viewRow(i)); } return eigenMap; } In case my problem is unclear, here's some context, I have an input matrix X and I want to find eigenvalues/eigenvectors

eigenvectors and eigenvalues of a matrix

2014-01-06 Thread Tharindu Rusira
Hi, I am currently working with SingularValueDecomposition class and I like to clarify the following. My goal is to find eigenvalues and corresponding eigenvectors of a matrix. I know how to calculate eigenvalues and eigenvectors using svd but is there a way to keep track of which eigenvector

Re: eigenvectors and eigenvalues of a matrix

2014-01-06 Thread Ted Dunning
The order of the singular values and vectors should tell you. For others who might be curious, the singular value decomposition breaks a matrix A into three factors A = U S V' Both U and V are orthonormal so that U' U = I and V' V = I. S is diagonal. An eigenvalue decomposition decomposes