Details of the LinearAlgebra Package - Maple Programming Help

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Details of the LinearAlgebra Package

 

Basic Information

Description

Accessing LinearAlgebra Package Commands

List of LinearAlgebra Package Commands

Examples

Basic Information

• 

This help page contains complete information about the LinearAlgebra package. For basic information on the LinearAlgebra package, see the LinearAlgebra help page.

Description

• 

The LinearAlgebra package is an efficient and robust suite of commands for performing computational linear algebra.

• 

LinearAlgebra routines operate on three principal data structures: Matrices, Vectors, and scalars.  For more information, see the Construct a Matrix, Construct a Vector, and About Data Structures in the LinearAlgebra Package help pages.

• 

Full rectangular and sparse matrices are fully supported at the data structure level, as well as upper and lower triangular matrices, unit triangular matrices, banded matrices, and a variety of others. Further, symmetric, skew-symmetric, hermitian, and skew-hermitian are known qualifiers that are used appropriately to reduce storage and select amongst algorithms.  For more information, see the Shapes and Storage Modes for Matrices and Vectors help page.

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The following data types are handled efficiently: hardware floating-point numbers (both real and complex), hardware integers of various sizes, arbitrary-precision floating-point numbers (both real and complex), and general symbolic expressions. For increased compatibility with external routines, matrices can be stored in either C or Fortran order.

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The LinearAlgebra package includes a subpackage, Modular, which provides a highly efficient suite of programmer tools for performing dense linear algebra computations in Z/m, the integers modulo m over the positive range.  For more information, see LinearAlgebra[Modular].

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The LinearAlgebra package includes a subpackage, Generic, for computing with generic implementations of algorithms for linear algebra over fields, Euclidean domains, integral domains and rings. For more information, see LinearAlgebra[Generic].

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The LinearAlgebra and VectorCalculus packages supersede the deprecated linalg package. For information illustrating the differences between these packages, see the Linear Algebra Computations in Maple help page.  For an example worksheet on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

Accessing LinearAlgebra Package Commands

• 

Each command in the LinearAlgebra package can be accessed by using either the long form or the short form of the command name in the command calling sequence.

  

As the underlying implementation of the LinearAlgebra package is a module, it is also possible to use the form LinearAlgebra:-command to access a command from the package. For more information,  see Module Members.

List of LinearAlgebra Package Commands

  

The following is a list of available commands.

`&x`

Add

Adjoint

BackwardSubstitute

BandMatrix

Basis

BezoutMatrix

BidiagonalForm

BilinearForm

CARE

CharacteristicMatrix

CharacteristicPolynomial

Column

ColumnDimension

ColumnOperation

ColumnSpace

CompanionMatrix

CompressedSparseForm

ConditionNumber

ConstantMatrix

ConstantVector

Copy

CreatePermutation

CrossProduct

DARE

DeleteColumn

DeleteRow

Determinant

Diagonal

DiagonalMatrix

Dimension

DotProduct

EigenConditionNumbers

Eigenvalues

Eigenvectors

Equal

ForwardSubstitute

FrobeniusForm

FromCompressedSparseForm

FromSplitForm

GaussianElimination

GenerateEquations

GenerateMatrix

GetResultDataType

GetResultShape

GivensRotationMatrix

GramSchmidt

HankelMatrix

HermiteForm

HermitianTranspose

HessenbergForm

HilbertMatrix

HouseholderMatrix

IdentityMatrix

IntersectionBasis

IsDefinite

IsOrthogonal

IsSimilar

IsUnitary

JordanBlockMatrix

JordanForm

KroneckerProduct

LeastSquares

LinearSolve

LUDecomposition

LyapunovSolve

Map

Map2

MatrixAdd

MatrixExponential

MatrixFunction

MatrixInverse

MatrixMatrixMultiply

MatrixNorm

MatrixPower

MatrixScalarMultiply

MatrixVectorMultiply

MinimalPolynomial

Minor

Multiply

Norm

Normalize

NullSpace

OuterProductMatrix

Permanent

Pivot

PopovForm

ProjectionMatrix

QRDecomposition

RandomMatrix

RandomVector

Rank

RationalCanonicalForm

ReducedRowEchelonForm

Row

RowDimension

RowOperation

RowSpace

ScalarMatrix

ScalarMultiply

ScalarVector

SchurForm

SingularValues

SmithForm

SplitForm

StronglyConnectedBlocks

SubMatrix

SubVector

SumBasis

SylvesterMatrix

SylvesterSolve

ToeplitzMatrix

Trace

Transpose

TridiagonalForm

UnitVector

VandermondeMatrix

VectorAdd

VectorAngle

VectorMatrixMultiply

VectorNorm

VectorScalarMultiply

ZeroMatrix

ZeroVector

Zip

 

 

 

  

To display the help page for a particular LinearAlgebra command, see Getting Help with a Command in a Package.

Examples

withLinearAlgebra:

Construct a Matrix using shortcut notation

1|2|3,4|5|6

123456

(1)

Construct a Matrix with optional construction parameters

Matrix1,2,3,4,5,6,readonly=true

123456

(2)

Create a random Matrix.

ARandomMatrix2,3

A:=994431299267

(3)

The inplace option saves memory and prevents creating new variable names for intermediate results.

RowOperationA,1,2,inplace

299267994431

(4)

A

299267994431

(5)

Create an upper triangular Matrix.

MRandomMatrix5,outputoptions=shape=triangularupper

M:=6982747403227276009327570007798000033

(6)

Define two matrices.

AMatrix2,5,1,3:

BMatrix6,11,9,21:

Performing calculations in a casual usage scenario accepts optional arguments in any order.

MatrixAddA,B,1,1

46818

(7)

See Also

examples/LA_Linear_Solve

examples/LA_NAG

examples/LA_options

LAIndex

module

UsingPackages

with

 


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