Geodesic
The equation $XA+AX^*=0$ and the dimension of *congruence orbits
The electronic journal of linear algebra, Tome 22 (2011), pp. 448-465.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We solve the matrix equation XA + AX * = 0, where A $\in C$ n $\times n$ 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 $\times n$ . As an application, we determine the generic canonical structure for * congruence in C n $\times n$ and also the generic Kronecker canonical form of * palindromic pencils $A + \lambda A$ * .
Classification : 15A24, 15A21
Keywords: canonical forms for * congruence, * congruence, codimension, matrix equations, orbits, * palindromic pencils 
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     author = {De Ter\'an, Fernando and Dopico, Froil\'an M.},
     title = {The equation $XA+AX^*=0$ and the dimension of *congruence orbits},
     journal = {The electronic journal of linear algebra},
     pages = {448--465},
     publisher = {mathdoc},
     volume = {22},
     year = {2011},
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De Terán, Fernando; Dopico, Froilán M. The equation $XA+AX^*=0$ and the dimension of *congruence orbits. The electronic journal of linear algebra, Tome 22 (2011), pp. 448-465. http://geodesic.mathdoc.fr/item/ELA_2011__22__a50/