### Chapter 6: Eigenvalue and Least-squares Problems

 Chapter Introduction Module 6.1: nag_sym_eig - Standard Symmetric Eigenvalue Problems nag_sym_eig_all All eigenvalues, and optionally eigenvectors, of a real symmetric or complex Hermitian matrix nag_sym_eig_sel Selected eigenvalues, and optionally the corresponding eigenvectors, of a real symmetric or complex Hermitian matrix nag_sym_tridiag_reduc Reduction of a real symmetric or complex Hermitian matrix to real symmetric tridiagonal form nag_sym_tridiag_orth Form or apply the transformation matrix determined by nag_sym_tridiag_reduc nag_sym_tridiag_eig_all All eigenvalues, and optionally eigenvectors, of a real symmetric tridiagonal matrix nag_sym_tridiag_eig_val Selected eigenvalues of a real symmetric tridiagonal matrix nag_sym_tridiag_eig_vec Selected eigenvectors of a real symmetric tridiagonal matrix Examples Module 6.2: nag_nsym_eig - Standard Nonsymmetric Eigenvalue Problems nag_nsym_eig_all All eigenvalues, and optionally eigenvectors, of a general real or complex matrix nag_schur_fac Schur factorization of a general real or complex matrix Examples Module 6.3: nag_svd - Singular Value Decomposition (SVD) nag_gen_svd Singular value decomposition of a general real or complex matrix nag_gen_bidiag_reduc Reduction of a general real or complex matrix to real bidiagonal form nag_bidiag_svd Singular value decomposition of a real bidiagonal matrix Examples Module 6.4: nag_lin_lsq - Linear Least-squares problems nag_lin_lsq_sol Solves a real or complex linear least-squares problem nag_lin_lsq_sol_svd Solves a real or complex linear least-squares problem, assuming that a singular value decomposition of the coefficient matrix has already been computed nag_qr_fac QR factorization of a general real or complex matrix nag_qr_orth Form or apply the matrix determined by nag_qr_fac nag_lin_lsq_sol_qr Solves a real or complex linear least-squares problem, assuming that the factorization of the coefficient matrix has already been computed nag_lin_lsq_sol_qr_svd Solves a real or complex linear least-squares problem using the SVD, assuming that the QR factorization of the coefficient matrix has already been computed Examples Module 6.5: nag_sym_gen_eig - Symmetric-definite Generalized Eigenvalue Problems nag_sym_gen_eig_all All eigenvalues, and optionally eigenvectors, of a real symmetric-definite or complex Hermitian-definite generalized eigenvalue problem nag_sym_gen_eig_sel Selected eigenvalues, and optionally the corresponding eigenvectors, of a real symmetric-definite or complex Hermitian-definite generalized eigenvalue problem Examples Module 6.6: nag_nsym_gen_eig - Nonsymmetric Generalized Eigenvalue Problems nag_nsym_gen_eig_all All eigenvalues, and optionally eigenvectors, of a real or complex nonsymmetric generalized eigenvalue problem nag_gen_schur_fac Generalized Schur factorization of a real or complex matrix pencil Examples