- LINEAR & MULTILINEAR ALGEBRA Journal
- December 2013
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- We give a complete solution of the matrix equation AX+BX=0, where A, BCmxn are two given matrices, XCnxn is an unknown matrix, and denotes the transpose or the conjugate transpose. We provide a closed formula for the dimension of the solution space of the equation in terms of the Kronecker canonical form of the matrix pencil A+B, and we also provide an expression for the solution X in terms of this canonical form, together with two invertible matrices leading A+B to the canonical form by strict equivalence.
- matrix equations; matrix pencils; kronecker canonical form; transpose; conjugate transpose sylvester equation