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, seeMatrices in the MATLAB Environment.

Funktionen

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Linear Equations

`mldivide`	Solve systems of linear equationsAx = Bforx
`mrdivide`	Solve systems of linear equationsxA = Bforx
`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 equationAX + XB = CforX

Eigenvalues and Singular Values

`eig`	Eigenvalues and eigenvectors
`eigs`	的子集eigenvalues and eigenvectors
`balance`	Diagonal scaling to improve eigenvalue accuracy
`svd`	Singular value decomposition
`pagesvd`	Page-wise singular value decomposition
`圣言会`	的子集singular values and vectors
`圣言会ketch`	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

Matrix Decomposition

`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

Matrix Operations

`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

Matrix Structure

`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

Matrix Properties

`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