21 citations · 35 across the 15 of their papers we have counts for
15 papers
Reverse order laws for generalized inverses of products of two or three matrices with applications
Yongge Tian
One of the fundamental research problems in the theory of generalized inverses of matrices is to establish reverse order laws for generalized inverses of matrix products. Under the…
Twists of two or multiple idempotent matrices
Yongge Tian
In this article, we revisit some block matrix construction methods and use them to derive various general expansion formulas for calculating the ranks of matrix expressions. As app…
How to solve three fundamental linear matrix inequalities in the Löwner partial ordering
Yongge Tian
This paper shows how to solve analytically the three fundamental linear matrix inequalities $$ AXB \succcurlyeq C \, (\succ C), \ \ AXA^*\succcurlyeq B \, (\succ B), \ \ AX +(AX)^{…
Solutions of the matrix inequalities in the minus partial ordering and in the Löwner partial ordering
Yongge Tian
Two matrices and of the same size are said to satisfy the minus partial ordering, denoted by , iff the rank subtractivity equality ${\rm rank}(\, A - B\,)…
Equalities and inequalities for Hermitian solutions and Hermitian definite solutions of the two matrix equations and
Yongge Tian
This paper studies algebraic properties of Hermitian solutions and Hermitian definite solutions of the two types of matrix equation and . We first establish a v…
Analytical formulas for calculating the extremal ranks of the matrix-valued function when the rank of is fixed
Yongge Tian
One of the simplest matrix-valued function with a single variable matrix is given by . In this this note, analytical formulas are established for calculating the maxim…