Linear Algebra

Linear equations, eigenvalues, singular values, decomposition, matrix operations, matrix structure

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.

Funzioni

espandi tutto

 mldivide Solve systems of linear equations Ax = B for x mrdivide Solve systems of linear equations xA = B for x decomposition Matrix decomposition for solving linear systems lsqminnorm Minimum norm least-squares solution to linear equation linsolve Solve linear system of equations inv Matrix inverse pinv Moore-Penrose pseudoinverse lscov Least-squares solution in presence of known covariance lsqnonneg Solve nonnegative linear least-squares problem sylvester Solve Sylvester equation AX + XB = C for X
 eig Eigenvalues and eigenvectors eigs Subset of eigenvalues and eigenvectors balance Diagonal scaling to improve eigenvalue accuracy svd Singular value decomposition pagesvd Page-wise singular value decomposition svds Subset of singular values and vectors svdsketch Compute SVD of low-rank matrix sketch gsvd Generalized singular value decomposition ordeig Eigenvalues of quasitriangular matrices ordqz Reorder eigenvalues in QZ factorization ordschur Reorder eigenvalues in Schur factorization polyeig Polynomial eigenvalue problem qz QZ factorization for generalized eigenvalues hess Hessenberg form of matrix schur Schur decomposition rsf2csf Convert real Schur form to complex Schur form cdf2rdf Convert complex diagonal form to real block diagonal form
 lu LU matrix factorization ldl Block LDL' factorization for Hermitian indefinite matrices chol Cholesky factorization cholupdate Rank 1 update to Cholesky factorization qr QR decomposition qrdelete Remove column or row from QR factorization qrinsert Insert column or row into QR factorization qrupdate Rank 1 update to QR factorization planerot Givens plane rotation
 transpose Transpose vector or matrix ctranspose Complex conjugate transpose pagetranspose Page-wise transpose pagectranspose Page-wise complex conjugate transpose mtimes Matrix multiplication pagemtimes Page-wise matrix multiplication mpower Matrix power sqrtm Matrix square root expm Matrix exponential logm Matrix logarithm funm Evaluate general matrix function kron Kronecker tensor product cross Cross product dot Dot product
 bandwidth Lower and upper matrix bandwidth tril Lower triangular part of matrix triu Upper triangular part of matrix isbanded Determine if matrix is within specific bandwidth isdiag Determine if matrix is diagonal ishermitian Determine if matrix is Hermitian or skew-Hermitian issymmetric Determine if matrix is symmetric or skew-symmetric istril Determine if matrix is lower triangular istriu Determine if matrix is upper triangular
 norm Vector and matrix norms normest 2-norm estimate vecnorm Vector-wise norm cond Condition number for inversion condest 1-norm condition number estimate rcond Reciprocal condition number condeig Condition number with respect to eigenvalues det Matrix determinant null Null space of matrix orth Orthonormal basis for range of matrix rank Rank of matrix rref Reduced row echelon form (Gauss-Jordan elimination) trace Sum of diagonal elements subspace Angle between two subspaces

Argomenti

Matrices in the MATLAB Environment

Matrix creation and basic operations.

Systems of Linear Equations

Solve several types of systems of linear equations.

Eigenvalues

Eigenvalue and eigenvector computation.

Singular Values

Singular value decomposition (SVD).

Factorizations

Common matrix factorizations (Cholesky, LU, QR).

Matrix Exponentials

This example shows 3 of the 19 ways to compute the exponential of a matrix.

Determine Whether Matrix Is Symmetric Positive Definite

This topic explains how to use the chol and eig functions to determine whether a matrix is symmetric positive definite (a symmetric matrix with all positive eigenvalues).

LAPACK in MATLAB

LAPACK provides a foundation of routines for linear algebra functions and matrix computations in MATLAB.