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LinearAlgebra

  

MatrixFunction

  

determine F(A) for a square Matrix A

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MatrixFunction(A, F, x, options)

Parameters

A

-

square Matrix

F

-

analytic expression

x

-

variable; specifies the indeterminate in f to use in the Matrix polynomial construction

options

-

(optional); constructor options for the result object

Description

• 

The MatrixFunction(A) command returns the Matrix obtained by interpolating [lambda, F( lambda )] for each of the eigenvalues lambda of A, including multiplicities. Here the Matrix polynomial is r(lambda) = F(lambda) - p(lambda)*q(lambda) where p(x) is the characteristic polynomial, q(lambda) is the quotient, and r(lambda) is the remainder.

• 

The options option provides additional information (readonly, shape, storage, order, datatype, and attributes) to the Matrix constructor that builds the result. These options may also be provided in the form outputoptions=[...], where [...] represents a Maple list.  If a constructor option is provided in both the calling sequence directly and in an outputoptions option, the latter takes precedence (regardless of the order).

• 

This function is part of the LinearAlgebra package, and so it can be used in the form MatrixFunction(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[MatrixFunction](..).

Examples

withLinearAlgebra:

AMatrix13,10,21,16

A:=13102116

(1)

MatrixFunctionA,v2,v

41306346

(2)

MatrixFunctionA,sinx,x

15sin114sin210sin2+10sin121sin221sin114sin1+15sin2

(3)

MatrixFunctionA,ⅇx,x

15ⅇ14ⅇ210ⅇ2+10ⅇ21ⅇ221ⅇ14ⅇ+15ⅇ2

(4)

MatrixExponentialA,t

15ⅇt14ⅇ2t10ⅇ2t+10ⅇt21ⅇ2t21ⅇt14ⅇt+15ⅇ2t

(5)

MatrixFunctionA,ⅇxt,x

15ⅇt14ⅇ2t10ⅇ2t+10ⅇt21ⅇ2t21ⅇt14ⅇt+15ⅇ2t

(6)

MatrixFunctionA,lnx,x,readonly

14ln210ln221ln215ln2

(7)

BMatrixy

B:=y

(8)

MatrixExponentialB

ⅇy

(9)

MatrixFunctionB,ⅇy,y

ⅇy

(10)

MatrixFunctionB,ⅇy

ⅇy

(11)

See Also

indets

LinearAlgebra

LinearAlgebra[MatrixExponential]

LinearAlgebra[MatrixPower]

Matrix

Vector

 


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