Eigendecomposition, Singular-Values and the Power Method
Perform principal component analysis
Perform singular values decomposition
Compute the eigenvectors matrix of a square symmetric matrix
Compute the eigenvectors of a square symmetric matrix
Modified Gram-Schmidt orthogonalization of a matrix
Modified Gram-Schmidt orthogonalization of a matrix
Eigendecomposition, Singular-Values and the Power Method
For a data matrix with m rows and n columns (m>=n), the power method is used to compute, simultaneously, the eigendecomposition of a square symmetric matrix. This result is used to obtain the singular value decomposition (SVD) and the principal component analysis (PCA) results. Compared to the classical SVD method, the first r singular values can be computed.