On the Rodman-Shalom conjecture regarding the Jordan form of completions of partial upper triangular matrices
Year: 1998
Type: article
Abstract: 168:221{249, 1992] conjecture the following statement: Let A be a lower irreducible partial upper triangular n n matrix over F such that trace(A) = 0 .L e t n 1 n 2 np 1 be a set of p positive i n tegers such that p X i=1 n i = n.There exists a nilpotent completion Ac of A whose Jordan form consists of p blocks of sizes n i n i , i = 1 ;2; : : : ; pif and only if r(A k ) X i:n i k (n i , k), k = 1 ;2; : : : ; n 1 .In this paper this conjecture is solved in two cases: when the minimal rank of A is 2, and for matrices of size 5 5.
Authors: Cristina Jordan, Juan Torregrosa, Ana Urbano
Institution: Universitat Politècnica de València
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W796572148