The Structure of Symmetric Solutions of the Matrix Equation AX = B over a Principal Ideal Domain | Zendy

В. М. Прокіп | Zendy

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The Structure of Symmetric Solutions of the Matrix Equation AX = B over a Principal Ideal Domain

Author(s) -

В. М. Прокіп

Publication year - 2017

Publication title -

international journal of analysis

Language(s) - English

Resource type - Journals

eISSN - 2314-4998

pISSN - 2314-498X

DOI - 10.1155/2017/2867354

Subject(s) - mathematics , symmetric matrix , matrix (chemical analysis) , centrosymmetric matrix , domain (mathematical analysis) , ideal (ethics) , combinatorics , pure mathematics , mathematical analysis , square matrix , eigenvalues and eigenvectors , physics , philosophy , materials science , epistemology , quantum mechanics , composite material

We investigate the structure of symmetric solutions of the matrix equation AX=B, where A and B are m-by-n matrices over a principal ideal domain R and X is unknown n-by-n matrix over R. We prove that matrix equation AX=B over R has a symmetric solution if and only if equation AX=B has a solution over R and the matrix ABT is symmetric. If symmetric solution exists we propose the method for its construction

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