mathjs/docs/reference/functions/sylvester.md

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Function sylvester #

Solves the real-valued Sylvester equation AX+XB=C for X, where A, B and C are matrices of appropriate dimensions, being A and B squared. Notice that other equivalent definitions for the Sylvester equation exist and this function assumes the one presented in the original publication of the the Bartels- Stewart algorithm, which is implemented by this function. https://en.wikipedia.org/wiki/Sylvester_equation

Syntax #

math.sylvester(A, B, C)

Parameters #

Parameter	Type	Description
A	Matrix | Array	Matrix A
B	Matrix | Array	Matrix B
C	Matrix | Array	Matrix C

Returns #

Type	Description
Matrix | Array	Matrix X, solving the Sylvester equation

Throws #

Type	Description

Examples #

const A = [[-1, -2], [1, 1]]
const B = [[2, -1], [1, -2]]
const C = [[-3, 2], [3, 0]]
math.sylvester(A, B, C)      // returns DenseMatrix [[-0.25, 0.25], [1.5, -1.25]]

See also #

schur, lyap