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suivant: Basis of a linear monter: Linear algebra précédent: Transconjugate of a matrix   Table des matières   Index


Equivalent matrix : changebase

changebase takes as argument a matrix A and a change-of-basis matrix P.
changebase returns the matrix B such that B = P-1AP.
Input :
changebase([[1,2],[3,4]],[[1,0],[0,1]])
Output :
[[1,2],[3,4]]
Input :
changebase([[1,1],[0,1]],[[1,2],[3,4]])
Output :
[[-5,-8],[9/2,7]]
Indeed :

$\displaystyle \left[\vphantom{\begin{array}{rr} 1 & 2\\  3&4\end{array}}\right.$$\displaystyle \begin{array}{rr} 1 & 2\\  3&4\end{array}$$\displaystyle \left.\vphantom{\begin{array}{rr} 1 & 2\\  3&4\end{array}}\right]^{{{-1}}}_{{}}$*$\displaystyle \left[\vphantom{\begin{array}{rr}1 & 1\\  0&1\end{array}}\right.$$\displaystyle \begin{array}{rr}1 & 1\\  0&1\end{array}$$\displaystyle \left.\vphantom{\begin{array}{rr}1 & 1\\  0&1\end{array}}\right]$*$\displaystyle \left[\vphantom{\begin{array}{rr} 1 & 2\\  3&4\end{array}}\right.$$\displaystyle \begin{array}{rr} 1 & 2\\  3&4\end{array}$$\displaystyle \left.\vphantom{\begin{array}{rr}1 & 2\\  3&4\end{array}}\right]$ = $\displaystyle \left[\vphantom{\begin{array}{rr}-5 & -8\\  \frac{9}{2}&7\end{array}}\right.$$\displaystyle \begin{array}{rr}-5 & -8\\  \frac{9}{2}&7\end{array}$$\displaystyle \left.\vphantom{\begin{array}{rr}-5 & -8\\  \frac{9}{2}&7\end{array}}\right]$

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giac documentation written by Renée De Graeve and Bernard Parisse