Given a matrix A, is possible to rewrite A like:(adsbygoogle = window.adsbygoogle || []).push({});

##A = B D B^{-1}##

##

\begin{bmatrix}

a_{11} & a_{12} \\

a_{21} & a_{22} \\

\end{bmatrix}

=

\begin{bmatrix}

?_{11} & ?_{12} \\

?_{21} & ?_{22} \\

\end{bmatrix}

\begin{bmatrix}

\lambda_{1} & 0 \\

0 & \lambda_{2} \\

\end{bmatrix}

\begin{bmatrix}

?_{11} & ?_{12} \\

?_{21} & ?_{22} \\

\end{bmatrix}^{-1}

##

(if A is diagonalizable)

Being ##\lambda_i## the i-th root of the characterisc polynomial of A.

But, what is the definition of the matrix B in terms of A?

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# A = bdb⁻¹

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