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Mark44

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Two of my favorite areas of study are linear algebra and computer programming. In this article I combine these areas by using Python to confirm that a given matrix satisfies the Cayley-Hamilton theorem. The theorem due to Arthur Cayley and William Hamilton states that if ##f(\lambda) = \lambda^n + c_{n-1}\lambda^{n-1} + \dots + c_1\lambda + c_0## is the characteristic polynomial for a square matrixA, then A is a solution to this characteristic equation. That is, ##f(A) = A^n + c_{n-1}A^{n-1} + \dots + c_1A + c_0I = 0##. HereIis the identity matrix of order n,0is the zero matrix, also of order n.

Characteristic polynomial– the determinant |A– λI|, whereAis an n x n square matrix,Iis the n x n identity matrix, and λ is a scalar variable, real or complex. The characteristic polynomial for a square matrix is a function of the variable, λ...

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