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LinearAlgebra[SylvesterSolve] - solve the Sylvester matrix equation

Calling Sequence

SylvesterSolve( A, B, C )

SylvesterSolve( A, B, C, isgn )

SylvesterSolve( A, B, C, isgn, pert, outopts, tranA, schurA, tranB, schurB )

Parameters

A

-

Matrix ; first input matrix, of dimension m by m

B

-

Matrix ; second input matrix, of dimension n by n

C

-

Matrix ; third input matrix, of dimension m by n

isgn

-

(optional) {-1,1} ; indicate the sign of the term X . B (second term)

pert

-

(optional) perturb=truefalse; allow use of perturbed values

outopts

-

(optional); constructor options for Matrix output

tranA

-

(optional) `transpose[A]`={truefalse,identical(transpose,hermitiantranspose)} ; specify operation on A prior to solving

schurA

-

(optional) `Schur[A]`=truefalse ; specify whether A is in Schur form

tranB

-

(optional) `transpose[B]`={truefalse,identical(transpose,hermitiantranspose)} ; specify operation on B prior to solving

schurB

-

(optional) `Schur[B]`=truefalse ; specify whether B is in Schur form

Description

• 

The SylvesterSolve command computes the solution to the Sylvester matrix equationA.X+isgnX.B=scaleC 

• 

The returned solution is an expression sequence consisting of the Matrix X followed by the scalar scale.

• 

This routine operates in the floating-point domain. Hence, the entries in the Matrix arguments must necessarily be of type complex(numeric).

Examples

withLinearAlgebra:

A:=2,3,7|1,1,5|2,1,7:

C:=IdentityMatrix3:

SylvesterSolveA,A,C

0.1764705882352940.2500000000000000.01470588235294120.2058823529411761.1102230246251610-160.05882352941176470.3235294117647060.2500000000000000.0147058823529412,1.

(1)

SylvesterSolveA,A,C,`transpose[A]`=true

1.233124397299900.5122950819672120.2041947926711660.5122950819672120.9508196721311460.01229508196721310.2041947926711660.01229508196721320.0113307618129220,1.

(2)

B:=SchurFormA

B:=9.528843811700596.268667184636551.352529751625940.0.7644219058503002.984533166272960.0.9997453128531590.764421905850300

(3)

SylvesterSolveA,B,C

0.08940922659478330.05587742534520160.2187743916308710.02800305118675280.3100614472566390.1759686588373540.02939402996147810.2690874164105470.0792924182346903,1.

(4)

SylvesterSolveA,B,C,`Schur[B]`=true

0.08940922659478330.05587742534520160.2187743916308710.02800305118675280.3100614472566390.1759686588373540.02939402996147810.2690874164105470.0792924182346903,1.

(5)

See Also

LinearAlgebra, LinearAlgebra[LyapunovSolve], LinearAlgebra[SchurForm]


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