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function [S, N] = signm(A) %SIGNM Matrix sign decomposition. % [S, N] = SIGNM(A) is the matrix sign decomposition A = S*N, % computed via the Schur decomposition. % S is the matrix sign function, sign(A). % Reference: % N. J. Higham, The matrix sign decomposition and its relation to the % polar decomposition, Linear Algebra and Appl., 212/213:3-20, 1994. [Q, T] = schur(A,'complex'); S = Q * matsignt(T) * Q'; % Only problem with Schur method is possible nonzero imaginary part when % A is real. Next line takes care of that. if ~any(imag(A)), S = real(S); end if nargout == 2 N = S*A; end