Given a square matrix A, the condition that characterizes an eigenvalue, λ, is the existence of a nonzero vector x such that A x = λ x; this equation can be rewritten as follows:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]Ax=\lambda x[/itex]

[itex](A-\lambda )x[/itex] = 0

[itex](A-\lambda I )x[/itex] = 0 -------------------- 1

After the above process we find the determinant of [itex]A-\lambda I [/itex] and then equate it to 0.

det([itex]A-\lambda I [/itex]) = 0 -------------------- 2

Then from the above characteristic equation we find the Eigen values.

My question is how does the equation 1 imply the above condition 2

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# Homework Help: Regarding Eigen values Of a Matrix

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