Matrix diagonalization

An n×nn\times n matrix AA is diagonalizable if there exists an invertible matrix, PP, such that D=P1APD=P^{-1}AP is a diagonal matrix. The matrix, PP, is said to diagonalize AA.

Example

Consider A=[3234]A=\begin{bmatrix}3&2\\3&4\end{bmatrix}, P=[1213]P=\begin{bmatrix}-1&2\\1&3\end{bmatrix} , and D=[1006]D=\begin{bmatrix}1&0\\0&6\end{bmatrix}. We can verify that P1AP=DP^{-1}AP=D.

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