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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.


Matrix Operations

catConcatenate symbolic arrays along specified dimension
colonCreate symbolic vectors, array subscripting, and for-loop iterators
horzcatConcatenate symbolic arrays horizontally
numelNumber of elements of symbolic array
sizeSymbolic matrix dimensions
sortSort elements of symbolic vectors or matrices
vertcatConcatenate symbolic arrays vertically

Matrix Transformations

diagCreate or extract diagonals of symbolic matrices
reshapeReshape symbolic array
trilReturn lower triangular part of symbolic matrix
triuReturn upper triangular part of symbolic matrix

Solving Linear Equations

adjointAdjoint of symbolic square matrix
condCondition number of matrix
detCompute determinant of symbolic matrix
equationsToMatrixConvert set of linear equations to matrix form
invCompute symbolic matrix inverse
linsolveSolve linear system of equations given in matrix form
normNorm of matrix or vector
pinvMoore-Penrose inverse (pseudoinverse) of symbolic matrix
rankFind rank of symbolic matrix
rrefReduced row echelon form of matrix (Gauss-Jordan elimination)

Matrix Basis

colspaceColumn space of matrix
nullForm basis for null space of matrix
orthOrthonormal basis for range of symbolic matrix

Matrix Factorizations

cholCholesky factorization
luLU factorization
qrQR factorization
svdSingular value decomposition of symbolic matrix
charpolyCharacteristic polynomial of matrix
eigEigenvalues and eigenvectors of symbolic matrix
jordanJordan form of matrix
curlCurl of vector field
divergenceDivergence of vector field
gradientGradient vector of scalar function
hessianHessian matrix of scalar function
jacobianJacobian matrix
laplacianLaplacian of scalar function
potentialPotential of vector field
vectorPotentialVector potential of vector field

Normal Forms

hermiteFormHermite form of matrix
jordanJordan form of matrix
smithFormSmith form of matrix

Special Matrices

bernsteinMatrixBernstein matrix
toeplitzSymbolic Toeplitz matrix
expmMatrix exponential
funmGeneral matrix function
logmMatrix logarithm
sqrtmMatrix square root


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.


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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