Mathematics > Linear Algebra

73 functions in MATLAB › Mathematics > Linear Algebra.

`balance`	Balances a matrix by a diagonal similarity transformation to improve eigenvalue accuracy.
`bandwidth`	Lower and upper bandwidth of a matrix.
`cdf2rdf`	Converts a complex diagonal eigendecomposition to real block-diagonal form.
`chol`	Cholesky factorization of a symmetric positive definite matrix.
`cholupdate`	Rank-one update or downdate of a Cholesky factor.
`cond`	Condition number of a matrix with respect to inversion.
`condeig`	Condition numbers of the eigenvalues of a matrix.
`condest`	Estimate of the 1-norm condition number of a matrix.
`cross`	Cross product of two 3-element vectors.
`decomposition`	Matrix decomposition object for solving linear systems repeatedly.
`det`	Determinant of a square matrix.
`dot`	Dot product of two vectors.
`eig`	Eigenvalues and eigenvectors of a square matrix.
`eigs`	A few eigenvalues of a large matrix.
`expm`	Matrix exponential.
`expmv`	Product of a matrix exponential and a vector.
`funm`	Evaluates a general function of a square matrix.
`gsvd`	Generalized singular value decomposition of a pair of matrices.
`hess`	Hessenberg form of a square matrix.
`inv`	Inverse of a square matrix.
`isbanded`	Tests whether a matrix lies within a given band.
`isdiag`	Tests whether a matrix is diagonal.
`ishermitian`	Tests whether a matrix is Hermitian or skew-Hermitian.
`isIllConditioned`	Tests whether a decomposition object represents an ill-conditioned matrix.
`issymmetric`	Tests whether a matrix is symmetric or skew-symmetric.
`istril`	Tests whether a matrix is lower triangular.
`istriu`	Tests whether a matrix is upper triangular.
`kron`	Kronecker tensor product of two matrices.
`ldl`	LDL factorization of a symmetric matrix.
`linsolve`	Solves a linear system, optionally telling it about the matrix structure.
`logm`	Matrix logarithm.
`lscov`	Least-squares solution with known covariance or weights.
`lsqminnorm`	Minimum-norm least-squares solution of a linear system.
`lsqnonneg`	Least squares with non-negativity constraints.
`lu`	LU factorization of a matrix.
`mldivide`	Left matrix division, the backslash operator, for solving linear systems.
`mpower`	Matrix power, the ^ operator.
`mrdivide`	Right matrix division, the / operator.
`mtimes`	Matrix multiplication, the * operator.
`norm`	Norm of a vector or matrix.
`normest`	Estimate of the 2-norm of a matrix.
`null`	Orthonormal basis of the null space of a matrix.
`ordeig`	Eigenvalues of a quasitriangular matrix in the order of the diagonal blocks.
`ordqz`	Reorders the eigenvalues in a QZ factorization.
`ordschur`	Reorders the eigenvalues in a Schur factorization.
`orth`	Orthonormal basis of the range of a matrix.
`pageeig`	Eigenvalues of each page of a 3-D array.
`pageinv`	Inverse of each page of a 3-D array.
`pagenorm`	Norm of each page of a 3-D array.
`pagesvd`	Singular value decomposition of every page of a 3-D array.
`pinv`	Moore-Penrose pseudoinverse of a matrix.
`planerot`	Givens plane rotation that zeroes the second component of a 2-element vector.
`qr`	QR factorization: an orthogonal factor Q and an upper-triangular factor R.
`qrdelete`	Updates a QR factorization after a column or row is removed from the matrix.
`qrinsert`	Updates a QR factorization after a column or row is inserted into the matrix.
`qrupdate`	Updates a QR factorization after a rank-1 change of the matrix.
`qz`	QZ (generalized Schur) factorization of a pair of square matrices.
`rank`	Rank of a matrix: the number of singular values above a tolerance.
`rcond`	Reciprocal condition number estimate of a square matrix in the 1-norm.
`rref`	Reduced row echelon form of a matrix, by Gauss-Jordan elimination.
`rsf2csf`	Converts a real Schur form into the complex, fully triangular Schur form.
`schur`	Schur decomposition of a square matrix.
`sqrtm`	Matrix square root: a matrix X with X*X equal to A.
`subspace`	Angle between two subspaces, given by the columns of two matrices.
`svd`	Singular value decomposition of a matrix.
`svdappend`	Updates an existing SVD after columns or rows are appended to the matrix.
`svds`	A few singular values and vectors of a matrix, typically a large sparse one.
`svdsketch`	Low-rank SVD approximation chosen automatically to meet a tolerance.
`sylvester`	Solves the Sylvester equation AX + XB = C.
`trace`	Sum of the diagonal elements of a square matrix.
`tril`	Lower triangular part of a matrix.
`triu`	Upper triangular part of a matrix.
`vecnorm`	Vector norm of each column or row of a matrix.