USEFUL MATLAB Functions

Linear Algebra

Matrix Analysis
cond Condition number with respect to inversion
condeig Condition number with respect to eigenvalues
det Determinant
norm Matrix or vector norm
normest Estimate matrix 2-norm
null Null space
orth Orthogonalization
rank Matrix rank
rcond Matrix reciprocal condition number estimate
rref Reduced row echelon form
subspace Angle between two subspaces
trace Sum of diagonal elements

Linear Equations

\ and /
Linear equation solution
chol
Cholesky factorization
cholinc
Incomplete Cholesky factorization
cond
Condition number with respect to inversion
condest
1-norm condition number estimate
funm
Evaluate general matrix function
inv
Matrix inverse
linsolve
Solve linear systems of equations
lscov
Least squares solution in presence of known covariance
lsqnonneg
Nonnegative least squares
lu
LU matrix factorization
luinc
Incomplete LU factorization
pinv
Moore-Penrose pseudoinverse of matrix
qr
Orthogonal-triangular decomposition
rcond
Matrix reciprocal condition number estimate

Eigenvalues and Singular Values

balance
Improve accuracy of computed eigenvalues
cdf2rdf
Convert complex diagonal form to real block diagonal form
condeig
Condition number with respect to eigenvalues
eig
Find eigenvalues and eigenvectors
eigs
Find largest eigenvalues and eigenvectors of sparse matrix
gsvd
Generalized singular value decomposition
hess
Hessenberg form of matrix
ordeig
Eigenvalues of quasitriangular matrices
ordqz
Reorder eigenvalues in QZ factorization
ordschur
Reorder eigenvalues in Schur factorization
poly
Polynomial with specified roots
polyeig
Polynomial eigenvalue problem
qz
QZ factorization for generalized eigenvalues
rsf2csf
Convert real Schur form to complex Schur form
schur
Schur decomposition
svd
Singular value decomposition
svds
Singular values and vectors of sparse matrix

Matrix Logarithms and Exponentials

expm
Matrix exponential
logm
Matrix logarithm
sqrtm
Matrix square root

Factorization

balance
Diagonal scaling to improve eigenvalue accuracy
cdf2rdf
Complex diagonal form to real block diagonal form
chol
Cholesky factorization
cholinc
Incomplete Cholesky factorization
cholupdate
Rank 1 update to Cholesky factorization
lu
LU matrix factorization
luinc
Incomplete LU factorization
planerot
Givens plane rotation
qr
Orthogonal-triangular decomposition
qrdelete
Delete column or row from QR factorization
qrinsert
Insert column or row into QR factorization
qrupdate
Rank 1 update to QR factorization
qz
QZ factorization for generalized eigenvalues
rsf2csf
Real block diagonal form to complex diagonal form