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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线性方程组

`mldivide`	Solve systems of linear equationsAx = Bforx
`mrdivide`	Solve systems of linear equationsxA = Bforx
`decomposition`	用于求解线性系统的矩阵分解
`lsqminnorm`	Minimum norm least-squares solution to linear equation
`linsolve`	求解方程的线性系统
`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`	特征值和特征向量
`eigs`	Subset of eigenvalues 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
`svdsketch`	Compute SVD of low-rank matrix sketch
`gsvd`	Generalized singular value decomposition
`ordeig`	Eigenvalues of quasitriangular matrices
`ordqz`	QZ分解中的特征值重新排序
`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`	将复杂的对角线形式转换为真实的块对角线形式

Matrix Decomposition

`鲁`	lu矩阵分解
`LDL`	Block LDL' factorization for Hermitian indefinite matrices
`chol`	Cholesky factorization
`cholupdate`	Rank 1 update to Cholesky factorization
`qr`	QR分解
`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平面旋转

矩阵操作

`转置`	Transpose vector or matrix
`ctranspose`	复杂的共轭转置
`pagetranspose`	Page-wise transpose
`pagectranspose`	页面综合偶联的转置
`mtimes`	Matrix multiplication
`pagemtimes`	页面矩阵乘法
`mpower`	Matrix power
`SQRTM`	矩阵平方根
`expm`	矩阵指数
`logm`	矩阵对数
`funm`	Evaluate general matrix function
`克朗`	Kronecker tensor product
`叉`	Cross product
`dot`	点产品

矩阵结构

`bandwidth`	Lower and upper matrix bandwidth
`tril`	矩阵的下三角部分
`triu`	矩阵的上三角部分
`isbanded`	Determine if matrix is within specific bandwidth
`isdiag`	Determine if matrix is diagonal
`ishermitian`	Determine if matrix is Hermitian or skew-Hermitian
`Issymmetric`	确定矩阵是对称还是偏斜的对称性
`伊斯特里`	确定矩阵是否较低三角形
`istriu`	Determine if matrix is upper triangular

Matrix Properties

`规范`	Vector and matrix norms
`规范est`	2-norm estimate
`vecnorm`	矢量规范
`cond`	Condition number for inversion
`秃鹰`	1符号条件号估计
`rcond`	Reciprocal condition number
`condeig`	Condition number with respect to eigenvalues
`det`	矩阵决定因素
`空值`	矩阵的空空间
`Orth`	矩阵范围的正顺序基础
`rank`	Rank of matrix
`rref`	Reduced row echelon form (Gauss-Jordan elimination)
`痕迹`	对角元素的总和
`子空间`	Angle between two subspaces