Arctic rank preservers of symmetric matrices and cybersecurity

A research the properties of Boolean arctic rank and perimeter and we classify the linear operators that preserve these matrix properties. The main objectives of this project are:

a. To investigate the properties on Boolean arctic rank of symmetric matrices. This Boolean symmetric matrix acts important role in linear algebra, graph theory, mathematical cryptography, engineering security technology and cyber security of data and information. In particular, we study the properties on the Boolean symmetric matrices and the linear operators that preserve this Boolean arctic rank and perimeter.

b. To investigate the properties of general Boolean symmetric matrix. In particular, we study the properties of general boolean arctic rank and we classify the linear operators that preserve this general Boolean arctic rank. We also investigate the properties of some matrix functions and determine the linear operators that preserve some matrix functions.

c. To study on the cyber security of data and information using the matrix theory. We hope to contribute the study of "linear preserver problems" by our research on the Boolean arctic rank and perimeter. We aim for applying these results to obtain theoretical basis for the researches of mathematical cryptography, engineering security technology and cyber security of data and information.