Non-Hermitian matrices of even order and neutral subspaces of half the dimension
Х. Д. Икрамов · Mathematical Notes · 2016
Consider the sesquilinearmatrix equation X * DX + AX + X * B + C = 0, where all the matrices are square and have the same order n . With this equation, we associate a block matrix M of double order 2 n . The solvability of the above equation turns out to be related to the existence of n -dimensional neutral subspaces for the matrix M . We indicate sufficiently general conditions ensuring the existence of such subspaces.