Overview of the LinearAlgebra Package
Interfaces to the LinearAlgebra Package
Essential LinearAlgebra Package Commands
The LinearAlgebra package offers routines to construct and manipulate Matrices and Vectors, compute standard operations, query results and solve linear algebra problems.
For a complete list of the routines in the LinearAlgebra package, see the Details of the LinearAlgebra Package help page.
Matrix, Vector, or an expression sequence of the two. Matrices 10 x 10 or smaller and vectors 10 x 1 and smaller display the corresponding Matrix or Vector in the Maple worksheet. Matrices and vectors larger then this display a placeholder as output. To see the entries or structured views of the Matrix or Vector, double-click the placeholder. For more details, see the browse Matrix help page.
Each command in the LinearAlgebra package is accessed by using either the long form or the short form of the command name in the command calling sequence. For more information, see the Using Packages help page.
Some routines in the LinearAlgebra package come with Maplet interfaces. To see the available interfaces, see the Maplets:-Examples:-LinearAlgebra help page.
Some routines in the LinearAlgebra package come with a task template to step you through the process of solving a linear algebra problem. For more information, see the Using Tasks help page.
For students learning the concepts presented in an introductory linear algebra course, see the Student:-LinearAlgebra help page.
return a basis for a vector space
construct the characteristic polynomial of a Matrix
compute the cross product of two Vectors
delete rows of a Matrix
compute the determinant of a Matrix
determine the dimension of a Matrix or a Vector
compute the dot product of two Vectors
compute the eigenvalues of a Matrix
compute the eigenvectors of a Matrix
perform Gaussian elimination on a Matrix
compute the least squares solutions to equations
solve the linear equations A . x = b
map a procedure onto an expression
compute the inverse of a square Matrix
compute the product of a Matrix and a scalar
compute a basis for the nullspace of a Matrix
construct a random Matrix
perform Gauss-Jordan elimination on a Matrix
construct a submatrix of a Matrix
compute the transpose of a Matrix
Construct a 5 x 5 Matrix.
M ≔ RandomMatrix⁡5
Construct a submatrix of the Matrix M, where the first list in the calling sequence selects corresponding row entries and the second list selects column entries.
Construct the Sylvester Matrix of two polynomials.
Compute the Eigenvectors of a Matrix.
Test if the Matrix M is orthogonal.
M ≔ Matrix⁡10⋅310,−1010,1010,10⋅310
Solve the system defined by Matrix M and Vector v.
M ≔ Matrix⁡1,1,3,−1,1,1,1,1,1,−2,1,−1,4,1,8,−1
v ≔ Vector⁡0,1,1,0
Construction of simple Matrices and Vectors, extraction of submatrices, transposition, basic arithmetic and computation of inner products can be done directly without use of commands in the LinearAlgebra package.
u ≔ Vector⁡1,3
v ≔ Vector⁡5,7
A ≔ Matrix⁡1,3,5,7
B ≔ Matrix⁡1,1,1,1
For more information including:
a complete list of the routines in the LinearAlgebra package
the supported data structures and data types
the different sets of commands based on usage scenario: casual use or programming use
the LinearAlgebra:-Modular subpackage for performing dense linear algebra computations in Z/m.
the LinearAlgebra:-Generic subpackage for computing with generic implementations of algorithms for linear algebra over fields, Euclidean domains, integral domains and rings.
see the Details of the LinearAlgebra Package help page.
Bivariate Polynomial Regression
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