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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

Matrix Operations

cat Concatenate symbolic arrays along specified dimension
colon Create symbolic vectors, array subscripting, and for-loop iterators
horzcat Concatenate symbolic arrays horizontally
numel Number of elements of symbolic array
size Symbolic matrix dimensions
sort Sort elements of symbolic vectors or matrices
vertcat Concatenate symbolic arrays vertically

Matrix Transformations

diag Create or extract diagonals of 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 Adjoint of symbolic square matrix
cond Condition number of matrix
det Compute determinant of symbolic matrix
equationsToMatrix Convert set of linear equations to matrix form
inv Compute symbolic matrix inverse
linsolve Solve linear system of equations given in matrix form
norm Norm of matrix or vector
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 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
svd Singular value decomposition of symbolic matrix
charpoly Characteristic polynomial of matrix
eig Eigenvalues and eigenvectors of symbolic matrix
jordan Jordan form of matrix
curl 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

Normal Forms

hermiteForm Hermite form of matrix
jordan Jordan form of matrix
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

Linear Algebraic Operations

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.

Linear Algebraic Operations

Linear algebra with symbolic expressions and functions.

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 (Jordon canonical form).

Featured Examples

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