INERTIA AND RANK CHARACTERIZATIONS OF SOME MATRIX EXPRESSIONS

In this paper the researchers consider the admissible inertias and ranks of the expressions ... and ... with unknowns X and Y in the four cases when these expressions are: (i) complex self-adjoint, (ii) complex skew-adjoint, (iii) real symmetric, (iv) real skew symmetric. They also provide a construction for X and Y to achieve the desired inertia/rank that uses only unitary/orthogonal transformation, thus leading to a numerically reliable construction. In addition, they look at related block matrix completion problems ... with either two diagonal unknown blocks and ... with an unknown off-diagonal block. Finally, they also provide all admissible ranks in the case when they drop any adjointness/symmetry constraint.(ProQuest: ... denotes formulae/symbols omitted.)