5.47.8 Equivalent matrix:
changebase
The
changebase
command changes a matrix to represent the same linear function in a different basis.
changebase
takes two arguments:
A
, a matrix.
P
, a change-of-basis matrix.
changebase(
A
,
P
)
returns the matrix
P
−1
AP
.
Examples.
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
9
2
7
⎤
⎥
⎥
⎥
⎥
⎦