Matrix::Sylvester Method

Matrix Struct

double Sylvester(TMtx *A, TMtx *B, TMtx *C, TSign ASign = TSign::siPlus, TMtxOperation AOp = TMtxOperation::opNone, TMtxOperation BOp = TMtxOperation::opNone) const;

Solves the Sylvester equation.

#NameTypeDescription
1ATMtx *
2BTMtx *
3CTMtx *
4ASign = TSign::siPlusTSign
5AOp = TMtxOperation::opNoneTMtxOperation
6BOp = TMtxOperation::opNoneTMtxOperation
Remarks:

Solves the Sylvester's equation

op(A)⋅X±X⋅op(B)=αC\text{op}(A)\cdot X \pm X\cdot \text{op}(B) = \alpha C

for real quasi-triangular or complex triangular matrices A and B. The solution (X) overwrites the C matrix. The AOp and BOp parameters indicate the TMtxOperation performed on A and B respectively. The TSign of the Sylvester equation is determined with the ASign parameter (siPlus for +, siMinus for -). The result of a Sylvester function is a scale factor a. The A and B matrices Matrix::Quadratic property must be true, otherwise an exception is raised.

Declared in Dew::Math::Matrix · Dew.Math/MtxExpr.h · Cross-compiler