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%% Matrix Evaluation of Characteristic Polynomial % Find the characteristic polynomial of a Pascal Matrix of order 4. % Copyright 2015 The MathWorks, Inc. X = pascal(4) p = poly(X) %% % The characteristic polynomial is % % $$p(x) = x^4 - 29x^3 + 72x^2 -29x + 1$$ % % Pascal matrices have the property that the vector of coefficients of the % characteristic polynomial is the same forward and backward (palindromic). %% % Substitute the matrix, |X|, into the characteristic equation, |p|. The % result is very close to being a zero matrix. This example is an instance % of the Cayley-Hamilton theorem, where a matrix satisfies its own % characteristic equation. Y = polyvalm(p,X)