Linear algebra functions in MATLAB® provide fast, numerically robust matrix calculations. Capabilities include a variety of matrix factorizations, linear equation solving, computation of eigenvalues or singular values, and more. For an introduction, see Matrices in the MATLAB Environment.
|Solve systems of linear equations Ax = B for x|
|Solve systems of linear equations xA = B for x|
|Matrix decomposition for solving linear systems|
|Minimum norm least-squares solution to linear equation|
|Solve linear system of equations|
|Least-squares solution in presence of known covariance|
|Solve nonnegative linear least-squares problem|
|Solve Sylvester equation AX + XB = C for X|
|Eigenvalues and eigenvectors|
|Subset of eigenvalues and eigenvectors|
|Diagonal scaling to improve eigenvalue accuracy|
|Singular value decomposition|
|Subset of singular values and vectors|
|Generalized singular value decomposition|
|Eigenvalues of quasitriangular matrices|
|Reorder eigenvalues in QZ factorization|
|Reorder eigenvalues in Schur factorization|
|Polynomial eigenvalue problem|
|QZ factorization for generalized eigenvalues|
|Hessenberg form of matrix|
|Convert real Schur form to complex Schur form|
|Convert complex diagonal form to real block diagonal form|
|LU matrix factorization|
|Block LDL' factorization for Hermitian indefinite matrices|
|Rank 1 update to Cholesky factorization|
|Remove column or row from QR factorization|
|Insert column or row into QR factorization|
|Rank 1 update to QR factorization|
|Givens plane rotation|
|Lower and upper matrix bandwidth|
|Lower triangular part of matrix|
|Upper triangular part of matrix|
|Determine if matrix is within specific bandwidth|
|Determine if matrix is diagonal|
|Determine if matrix is Hermitian or skew-Hermitian|
|Determine if matrix is symmetric or skew-symmetric|
|Determine if matrix is lower triangular|
|Determine if matrix is upper triangular|
|Vector and matrix norms|
|Condition number for inversion|
|1-norm condition number estimate|
|Reciprocal condition number|
|Condition number with respect to eigenvalues|
|Null space of matrix|
|Orthonormal basis for range of matrix|
|Rank of matrix|
|Reduced row echelon form (Gauss-Jordan elimination)|
|Sum of diagonal elements|
|Angle between two subspaces|
Matrix creation and basic operations.
Solve several types of systems of linear equations.
Eigenvalue and eigenvector computation.
Singular value decomposition (SVD).
Common matrix factorizations (Cholesky, LU, QR).
This example shows 3 of the 19 ways to compute the exponential of a matrix.
This topic explains how to use the
eig functions to determine whether a matrix is symmetric positive definite (a symmetric matrix with all positive eigenvalues).
LAPACK provides a foundation of routines for linear algebra functions and matrix computations in MATLAB.