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# More problems with general power of a matrix

Even though in version 8.2 the code for the general power of a matrix has been improved (c.f. question 41622), it still doesn't work in some cases, as i.e. this singular, diagonalizable matrix

A=matrix(QQbar,3,3,[[-2,-8,-12],[1,4,4],[0,0,1]])
k=var('k')
A**k


shows.

Concerning the remark in trac ticket 25520: Why not defining $0^x=1$ for $x\in {\bf N}$, which seems reasonable, since the number of functions $\emptyset \to \emptyset$ is 1?

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## 1 answer

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You are absolutely right, while being correct on positive integers, the expression is not correct when specialized to k=0:

sage: [B.subs(k=i) == A^i for i in range(20)]
[False,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True,
True]
sage: B.subs(k=0)
[ -1  -4  -8]
[1/2   2   2]
[  0   0   1]


Thanks for reporting, it is now trac ticket 25520

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Asked: 2018-06-06 09:12:15 -0500

Seen: 110 times

Last updated: Jun 17 '18