Block 2 x 2 Matrices Where Blocks Have Prescribed Digraphs
Start Date
April 2024
Location
2nd floor - Library
Abstract
This project investigates 2n x 2n matrices of the form C = C(A,B) where A, B are n x n matrices with real entries, I is the n x n identity matrix and O is the n x n zero matrix, using the relationship between the digraph of a matrix and its characteristic polynomial. Throughout the study, A and B are prescribed to have various known digraphs, such as stars, cycles, and paths. Digraph structures of A and B are then used to analyze the impact on the characteristic polynomial of C. Additionally, forms of A and B that result in a nilpotent matrix C are identified.
Block 2 x 2 Matrices Where Blocks Have Prescribed Digraphs
2nd floor - Library
This project investigates 2n x 2n matrices of the form C = C(A,B) where A, B are n x n matrices with real entries, I is the n x n identity matrix and O is the n x n zero matrix, using the relationship between the digraph of a matrix and its characteristic polynomial. Throughout the study, A and B are prescribed to have various known digraphs, such as stars, cycles, and paths. Digraph structures of A and B are then used to analyze the impact on the characteristic polynomial of C. Additionally, forms of A and B that result in a nilpotent matrix C are identified.
