ON SOME PROPERTIES OF SINGULAR SYMMETRIC MATRICES

In this paper, some properties of singular symmetric matrices are investigated in relation to the rectangular matrices. New theorems are proposed which show that a product of some rectangular matrices with their transposes yield always singular square matrices of the same rank. We also give some results regarding the possibility of splitting a singular symmetric square matrix into a product of a rectangular matrix with its transpose. This paper gives thus to the researchers new keys for providing solutions needed in the fields of IT, computer engineering, statistics and information security. © 2022, Politechnica University of Bucharest. All rights reserved.