Functions > Vector and Matrix > Array Characteristics > Eigenvectors and Eigenvalues
Eigenvectors and Eigenvalues
eigenvals(M)—Returns a vector whose elements are the eigenvalues of M.
eigenvec(M, z)—Returns a single normalized eigenvector associated with eigenvalue z of M. The eigenvector is normalized to unit length. The eigenvec functions uses an inverse iteration algorithm.
eigenvecs(M, ["L"])—Returns a matrix containing all normalized eigenvectors of the matrix M. The nth column of the returned matrix is an eigenvector corresponding to the nth eigenvalue returned by eigenvals. The right eigenvector is returned by default. The eigenvecs function can also return the left eigenvector, satisfying vH · M = z · vH, where H indicates conjugate transpose.
genvals(M, N)—Returns a vector of computed eigenvalues, vi, each of which satisfies the generalized eigenvalue problem M · x = vi · N · x for its associated eigenvector xi.
genvecs(M, N, ["L"])—Returns a matrix containing the normalized eigenvectors corresponding to the eigenvalues in v, the vector returned by genvals. The ith column of this matrix is the eigenvector x satisfying the generalized eigenvalue problem.
tr(M)—Returns the trace of M, that is, the sum of the elements along the diagonal of M. This is equal to the sum of the eigenvalues.
Arguments
M, N are square matrices of equal size and contain real or complex numbers.
"L" (optional) is a string. When used, the string "L" specifies the left eigenvector, and "R" the right. "R" is the default.
z is an eigenvalue of M.