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D.5.10.3 matrixLog
Procedure from library orbitparam.lib (see orbitparam_lib).
- Usage:
- matrixLog(A); A matrix.
- Assume:
- A-E is a nilpotent n x n matrix.
If the characteristic p of the ground field is positive, then n has to be
smaller than p.
- Return:
- matrix, log(A)
- Theory:
- We compute the power series, which terminates since A-E is nilpotent.
Example:
| | LIB "orbitparam.lib";
ring R = 0,(s,t),dp;
matrix A[3][3] = 1,s,st/2, 0,1,t, 0,0,1;
matrixLog(A);
==> _[1,1]=0
==> _[1,2]=s
==> _[1,3]=0
==> _[2,1]=0
==> _[2,2]=0
==> _[2,3]=t
==> _[3,1]=0
==> _[3,2]=0
==> _[3,3]=0
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