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Student[LinearAlgebra]

  

MatrixInverse

  

compute the inverse of a square Matrix or the Moore-Penrose pseudo-inverse of a Matrix

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

MatrixInverse(A, options)

Parameters

A

-

square Matrix

options

-

(optional) parameters; for a complete list, see LinearAlgebra[MatrixInverse]

Description

• 

The MatrixInverse(A) function, where A is a nonsingular square Matrix, returns the Matrix inverse A-1. If A is recognized as a singular Matrix, an error message is returned.

• 

If A is a nonsingular nxn Matrix, the inverse A-1 is computed such that A·A-1=I, where I is the nxn identity Matrix.

Examples

withStudentLinearAlgebra:

Ma,c|b,d

Mabcd

(1)

To compute the inverse of the 2x2 matrix, M, by hand:

1adbcd,c|b,a

dadbcbadbccadbcaadbc

(2)

M_IMatrixInverseM

M_Idadbcbadbccadbcaadbc

(3)

simplifyM·M_I

1001

(4)

The MatrixInverse command will not return a result for a non-square Matrix.

P1,2|3,4|1,7

P131247

(5)

For non-square matrices, use the Pseudoinverse command.

PseudoinverseP

910613184110619318135328159

(6)

P·PseudoinverseP

1001

(7)

Compatibility

• 

The Student[LinearAlgebra][MatrixInverse] command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

Student[LinearAlgebra]

Student[LinearAlgebra][Pseudoinverse]