A Derivation of Lower Triangular Interactor Matrix

The inverse along a lower triangular matrix

In this paper, we investigate the recently defined notion of inverse along an element in the context of matrices over a ring. Precisely, we study the inverse of a matrix along a lower triangular matrix, under some conditions.

Rigidity of a simple extended lower triangular matrix

For the all-ones lower triangular matrices, the upper and lower bounds on rigidity are known to match [13]. In this short note, we apply these techniques to the allones extended lower triangular matrices, to obtain upper and lower bounds with a small gap between the two; we show that the rigidity is θ( 2 r ).

THE INVERSE OF THE PASCAL LOWER TRIANGULAR MATRIX MODULO p

Let L(n)p be the Pascal lower triangular matrix with coefficients `i j ́ (mod p), 0 ≤ i, j < n. In this paper, we found the inverse of L(n)p modulo p. In fact, we generalize a result due to David Callan [4].

Differential Polynomial Rings of Triangular Matrix Rings

Strongly clean triangular matrix rings with endomorphisms

‎A ring $R$ is strongly clean provided that every element‎ ‎in $R$ is the sum of an idempotent and a unit that commutate‎. ‎Let‎ ‎$T_n(R,sigma)$ be the skew triangular matrix ring over a local‎ ‎ring $R$ where $sigma$ is an endomorphism of $R$‎. ‎We show that‎ ‎$T_2(R,sigma)$ is strongly clean if and only if for any $ain‎ ‎1+J(R)‎, ‎bin J(R)$‎, ‎$l_a-r_{sigma(b)}‎: ‎Rto R$ is surjective‎. ‎Furt...