线性代数

有关符号向量和矩阵的线性代数运算

线性代数是研究线性方程及其性质的学科。Symbolic Math Toolbox™ 提供用于求解线性方程组的函数。您还可以使用 Symbolic Math Toolbox 函数分析、变换和分解矩阵。

函数

`cat`	Concatenate symbolic arrays along specified dimension
`colon`	Create symbolic vectors, array subscripting, and `for`-loop iterators
`horzcat`	Concatenate symbolic arrays horizontally
`sort`	Sort elements of symbolic arrays
`vertcat`	Concatenate symbolic arrays vertically

`diag`	创建对角矩阵或从符号矩阵中获取对角线
`reshape`	Reshape symbolic array
`tril`	Return lower triangular part of symbolic matrix
`triu`	Return upper triangular part of symbolic matrix

`adjoint`	方阵的经典伴随矩阵（转置伴随矩阵）
`cond`	矩阵的条件数
`det`	Determinant of symbolic matrix
`equationsToMatrix`	Convert linear equations to matrix form
`inv`	Inverse of symbolic matrix
`linsolve`	求解矩阵形式的符号线性方程
`norm`	Norm of symbolic vector or matrix
`pinv`	Moore-Penrose inverse (pseudoinverse) of symbolic matrix
`rank`	Rank of symbolic matrix
`rref`	矩阵的简化行阶梯形（高斯-若尔当消元法）

`colspace`	矩阵列空间的基
`null`	Form basis for null space of matrix
`orth`	Orthonormal basis for range of symbolic matrix

`chol`	Cholesky factorization
`lu`	LU factorization
`qr`	QR decomposition of symbolic matrix
`svd`	Singular value decomposition of symbolic matrix

`charpoly`	矩阵的特征多项式
`eig`	Eigenvalues and eigenvectors of symbolic matrix
`jordan`	若尔当范式（若尔当标准形式）

`curl`	Curl of symbolic vector field
`divergence`	Divergence of symbolic vector field
`gradient`	Gradient vector of symbolic scalar field
`hessian`	符号标量函数的黑塞矩阵
`jacobian`	符号函数的雅可比矩阵
`laplacian`	Laplacian of symbolic field
`potential`	Potential of vector field
`vectorPotential`	Vector potential of vector field

`bernsteinMatrix`	Bernstein matrix
`toeplitz`	Symbolic Toeplitz matrix

`expm`	Matrix exponential of symbolic matrices
`funm`	General matrix function
`logm`	矩阵对数
`sqrtm`	Matrix square root

Symbolic Matrix Computation
This example shows how to perform simple matrix computations using Symbolic Math Toolbox™.
Linear Algebraic Operations
Perform linear algebra with symbolic expressions and functions.
求解线性方程组
求解矩阵形式或方程形式的线性方程组。
Basic Algebraic Operations
Perform algebraic operations on symbolic expressions and function.
Singular Value Decomposition
Singular value decomposition (SVD) of a matrix.
Eigenvalues
Find eigenvalues, characteristic polynomials, and determinants of matrices.
Jordan Canonical Form
Convert matrix to Jordan normal form (Jordan canonical form).
Eigenvalues of the Laplace Operator
This example shows how to solve the eigenvalue problem of the Laplace operator on an L-shaped region.
Hilbert Matrices and Their Inverses
This example shows how to compute the inverse of a Hilbert matrix using Symbolic Math Toolbox™.

Explore basic arbitrage concepts in a single-period, two-state asset portfolio.

Derive the symbolic stationary distribution of a trivial Markov chain by computing its eigen decomposition.

此示例说明了如何使用 Symbolic Math Toolbox™ 和矩阵在三维空间中进行旋转和变换。