Jean H. Bevis

The matrix equation A X – XB = C and its special cases

The consistency and solutions of the matrix equations

The rank of a graph after vertex addition

A\bar X - XB = C

Integer LU-factorizations

,

Pseudo-consimilarity and semi-consimilarity of complex matrices

A\bar X \pm XA^T = C

LDLT factorizations of adjacency matrices where D is block diagonal

,

Some Classes of Integral Matrices

A\bar X \pm XA^* = C

Nested Range Conditions for LU Factorizations of Integer Matrices

are characterized. As a consequence it is shown that

Conpseudosimilarity and consemisimilarity over a division ring

A^T

Integer generalized inverses of incidence matrices

(respectively,

Free gerbiers and nets

A^*