- #1
Jhenrique
- 685
- 4
Given a matrix A, is possible to rewrite A like:
##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?
##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?