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@jemoka / Jemoka Knowledge Base / wiki/concepts/characteristic_polynomial.md
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--- title: "characteristic polynomial" type: concept related: [Polynomial, Linear Map, Eigenvalue] source: https://www.jemoka.com/posts/kbhcharacteristic_polynomial/ confidence: high status: active --- The polynomial given by the determinant of: \begin{equation} det(A-\lambda I) \end{equation} for some Linear Map \(A\). Solutions for \(\lambda\) are the eigenvalues. This is because something is an eigenvalue IFF \((A-\lambda I)v = 0\) for some \(\lambda, v\), so we need \((A-\lambda I)\) to be singular. Characteristic polynomial of a 2x2 matrix is given by \(\lambda^{2}-tr(A)\lambda + det(A)\).