Аbout One Property of the Principal Leading Minors of the Lower Triangular Matrix

Abstract

In this paper, we considered a set of square matrices with positive angular minors. We implemented the similarity transformation triangular matrices with positive diagonal elements over the matrices. In Theorem 1, a sufficient condition was established to preserve the positivity of the angular minors of a square matrix with positive angular minors under the similarity transformation using the above-mentioned triangular matrices. In Theorem 2, a more rigorous sufficient condition was established for the preservation of a similar property with an additional restriction on the norm of the matrices under consideration.