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`	Create diagonal matrix or get diagonals from symbolic matrices
`reshape`	Reshape symbolic array
`tril`	Return lower triangular part of symbolic matrix
`triu`	Return upper triangular part of symbolic matrix

`adjoint`	Classical adjoint (adjugate) of square matrix
`cond`	Condition number of matrix
`det`	Determinant of symbolic matrix
`equationsToMatrix`	Convert linear equations to matrix form
`inv`	Inverse of symbolic matrix
`linsolve`	Solve symbolic linear equations in matrix form
`norm`	Norm of symbolic vector or matrix
`pinv`	Moore-Penrose inverse (pseudoinverse) of symbolic matrix
`rank`	Rank of symbolic matrix
`rref`	Reduced row echelon form of matrix (Gauss-Jordan elimination)

`colspace`	Basis for column space of matrix
`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`	Characteristic polynomial of matrix
`eig`	Eigenvalues and eigenvectors of symbolic matrix
`jordan`	Jordan normal form (Jordan canonical form)

`curl`	Curl of symbolic vector field
`divergence`	Divergence of symbolic vector field
`gradient`	Gradient vector of symbolic scalar field
`hessian`	Hessian matrix of symbolic scalar function
`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

`hermiteForm`	Hermite form of matrix
`jordan`	Jordan normal form (Jordan canonical form)
`smithForm`	Smith form of matrix

`bernsteinMatrix`	Bernstein matrix
`toeplitz`	Symbolic Toeplitz matrix

`expm`	Matrix exponential of symbolic matrices
`funm`	General matrix function
`logm`	Matrix logarithm
`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.
Solve System of Linear Equations
Solve systems of linear equations in matrix or equation form.
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.

Do rotations and transforms in 3-D using Symbolic Math Toolbox™ and matrices.