ON ESCHENBACH-JOHNSON CONJECTURE ABOUT DIAGONALIZABILITY
Eschenbach and Johnson proved that a necessary condition for a sign pattern A to allow diagonalizability is that (the minimum algebraic multiplicity of the eigenvalue 0 of A) ? (the maximum rank deficiency of A). They conjectured that this necessary condition is also sufficient [3]. In this paper, we give a complete answer to Eschenbach-Johnson?s conjecture: (1) For reducible sign patterns, the conjecture is true for and not true for (2) For irreducible sign patterns, the conjecture is true for and not true for
sign pattern, eigenvalue, diagonalizability.