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 :

⎡
⎢
⎣

1	2
3	4

⎤
⎥
⎦

⁻¹*

⎡
⎢
⎣

1	1
0	1

⎤
⎥
⎦

⎡
⎢
⎣

1	2
3	4

⎤
⎥
⎦

⎡
⎢
⎢
⎢
⎢
⎣

−5

−8

⎤
⎥
⎥
⎥
⎥
⎦