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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.

Functions

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mldivide Solve systems of linear equationsAx = Bforx
mrdivide Solve systems of linear equationsxA = Bforx
pagemldivide Page-wise left matrix divide
pagemrdivide Page-wise right matrix divide
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
pageinv Page-wise 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
eig Eigenvalues and eigenvectors
eigs 的特征子集values and eigenvectors
balance Diagonal scaling to improve eigenvalue accuracy
svd Singular value decomposition
pagesvd Page-wise singular value decomposition
圣言会 Subset of 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 求出广义特征值分解
hess 海塞nberg 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

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