Equivalent matrix

The changebase command changes a matrix to represent the same linear function in a different basis.

changebase([[1,2],[3,4]],[[1,0],[0,1]])

⎡
⎢
⎣

1	2
3	4

⎤
⎥
⎦

changebase([[1,1],[0,1]],[[1,2],[3,4]])

⎡
⎢
⎢
⎢
⎢
⎣

−5

−8

⎤
⎥
⎥
⎥
⎥
⎦

Indeed:

⎡
⎢
⎣

1	2
3	4

⎤
⎥
⎦

−1

⎡
⎢
⎣

1	1
0	1

⎤
⎥
⎦

⎡
⎢
⎣

1	2
3	4

⎤
⎥
⎦

⎡
⎢
⎢
⎢
⎢
⎣

−5

−8

⎤
⎥
⎥
⎥
⎥
⎦