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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

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Matrix Operations

 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 vectors or matrices 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 Convert linear equations to matrix form inv Inverse of symbolic matrix linsolve Solve linear equations 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 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 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 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 normal form (Jordan canonical form) 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

Symbolic Matrix Computation

This example shows how to perform simple matrix computations using Symbolic Math Toolbox™.

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 (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™.

Featured Examples

Mathematical Modeling with Symbolic Math Toolbox

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