The equation XA+AX*=0 and the dimension of *congruence orbits
Fernando De Terán, Froilán M. Dopico · Electronic Journal of Linear Algebra · 2011
We solve the matrix equation XA + AX * = 0, where A ∈ C n×n is an arbitrary given square matrix, and we compute the dimension of its solution space.This dimension coincides with the codimension of the tangent space of the * congruence orbit of A. Hence, we also obtain the (real) dimension of * congruence orbits in C n×n .As an application, we determine the generic canonical structure for * congruence in C n×n and also the generic Kronecker canonical form of * palindromic pencils A + λA * .