www.gusucode.com > matlab矩阵函数工具箱 > matlab矩阵函数工具箱/matlab矩阵函数工具箱/ascent_seq.m
function [d,a] = ascent_seq(A) %ASCENT_SEQ Ascent sequence for square (singular) matrix. % [d,a] = ASCENT_SEQ(A) returns symbolically computed % a(i) = dim(null(A^(i-1))) and the ascent sequence d = DIFF(a). % A has a square root if in the ascent sequence no two terms are % the same odd integer. % This function is intended for singular matrices of small % dimension with exactly known entries. % It requires the Symbolic Math Toolbox. if isempty(ver('symbolic')) error('The Symbolic Math Toolbox is required.') end n = length(A); a = zeros(n,1); A = sym(A); X = sym(eye(n)); for i = 2:n+1 X = X*A; N = null(X); if isempty(N), break, end a(i) = rank(N); end d = diff(a);