Main Content

Linear Algebra

Linear algebra operations on symbolic vectors and matrices

Linear algebra is the study of linear equations and their properties. Symbolic Math Toolbox™ provides functions to solve systems of linear equations. You can also analyze, transform, and decompose matrices using Symbolic Math Toolbox functions.

Functions

expand all

Matrix Operations

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

Matrix Transformations

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

Solving Linear Equations

adjoint Classical adjoint (adjugate) of square matrix
cond Condition number of matrix
det Determinant of symbolic matrix
equationsToMatrix 线性方程转化为矩阵形式
inv Inverse of symbolic matrix
linsolve Solve linear equations in matrix form
norm Norm of symbolic vector or matrix
pinv Moore-Penrose inverse (pseudoinverse) of symbolic matrix
rank Find rank of symbolic matrix
rref Reduced row echelon form of matrix (Gauss-Jordan elimination)

Matrix Basis

colspace Basis for column space of matrix
null Form basis for null space of matrix
orth Orthonormal basis for range of symbolic matrix

Matrix Factorizations

chol Cholesky factorization
lu LU factorization
qr QR factorization of symbolic matrix
svd Singular value decomposition of symbolic matrix
charpoly Characteristic polynomial of matrix
eig Eigenvalues and eigenvectors of symbolic matrix
jordan 约旦范式(约旦标准型)
旋度 Curl of vector field
divergence Divergence of vector field
gradient Gradient vector of scalar function
hessian Hessian matrix of scalar function
jacobian Jacobian matrix
laplacian Laplacian of scalar function
potential Potential of vector field
vectorPotential Vector potential of vector field

诺玛l Forms

hermiteForm Hermite form of matrix
jordan 约旦范式(约旦标准型)
smithForm Smith form of matrix

Special Matrices

bernsteinMatrix Bernstein matrix
toeplitz Symbolic Toeplitz matrix
expm Matrix exponential
funm General matrix function
logm Matrix logarithm
sqrtm Matrix square root

Topics