This problem is known as order determination, and amounts to estimating the rank of a matrix. Previous order-determination procedures rely either on the decreasing pattern, or elbow, of the ...

Paul A. White, The Computation of Eigenvalues and Eigenvectors of a Matrix, Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 4 (Dec., 1958), pp. 393-437 ...

You can divide many matrices into three matrices, one with the eigenvalues, one with the eigenvectors, and the inverse of the eigenvector one.

Eigenvectors are columns of numbers, and eigenvalues, scalars that are multiplied with the eigenvector, said Tao, who has published several papers about eigenvectors.

Eigenvalues and eigenvectors turn up in a wide range of contexts. Operations that stretch, shrink, shear, reflect or rotate objects in a linear way are described by matrices.