Solutions to a family of matrix equations by using the Kronecker matrix polynomials. (English) Zbl 1181.15020
Using the standard technique of Kronecker products, the authors give closed form solutions to the real generalized Sylvester matrix equation \(\sum_i A_iXF^i + \sum_k B_kYF^k = \sum_j E_jRF^j\), where \(A_i\), \(B_k\), \(E_j\) and \(F\), \(R\) are known matrices and the matrix pair \((X,Y)\) is the solution. A generalization of this equation is also considered.
Reviewer: Mihail M. Konstantinov (Sofia)
Keywords:
Sylvester matrix equations; closed form solutions; Kronecker matrix product; Kronecker matrix polynomials; coprime; linear system theoryReferences:
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