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Linear Algebra

Cayley- Hamilton Theorem: Every Matrix A is a root of its characterstic polynomial ∆(t).

Cayley- Hamilton Theorem: Every Matrix A is a root of its characterstic polynomial ∆(t). Proof: Let A be an arbitrary n- square matrix and let ∆(t) be its characterstic polynomial, say, ∆(t) = |tI-A| = tn +an-1tn-1+ …+a1t+a0 Now let B(t) denote the classical adjoint of the matrix tI-A. The ...

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