A Combinatorial Result on Block Matrices
S. M. Sadegh Tabatabaei Yazdi, Serap A. Savari
TL;DR
This paper establishes necessary and sufficient conditions for the existence of non-singular submatrices with specified row and column partition sizes in block matrices over a field.
Contribution
It provides a new combinatorial characterization for the invertibility of submatrices within partitioned matrices, advancing matrix theory.
Findings
Derived necessary and sufficient conditions for non-singular submatrices.
Extended classical results to block matrices with partition constraints.
Applicable to fields and matrices with structured partitions.
Abstract
Given a matrix with partitions of its rows and columns and entries from a field, we give the necessary and sufficient conditions that it has a non--singular submatrix with certain number of rows from each row partition and certain number of columns from each column partition.
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Taxonomy
Topicsgraph theory and CDMA systems · Graph Labeling and Dimension Problems · Graph theory and applications