Shorted operators of partitioned matrices and application

In this paper, our main objective is to study the effect of appending/deleting a column/row on the shorted operators. It turns out that for matrices A and B for which the shorted operator S(A|B) exists, S(A1|B1) of the matrix A1=[A:a] with respect to the matrix B1=[B:b], when it exists, is obtained by appending a suitable column to S(A|B). Moreover, if S(A1|B1) exists, then S(A|B) exists and is obtained from S(A1|B1) by dropping its last column. In the process, we study the effect of appending/deleting a column/row on the space pre-order and the parallel sum of parallel summable matrices. Finally, we specialize to the case of and matrices and study the effect of bordering (by an additional column and a row) on the shorted operator. We conclude the paper with an application to Linear Models with singular dispersion structure.