So I was trying to play around with matrix esponentials and proving a fundamental theorem of trigonometry analogon for this type structure. As it might happen, I ran across the problem in the title, while computing e^(zero matrix). I highly suppose it's the unit matrix, but is there a proper way to prove it?
Asked
Active
Viewed 248 times
1
-
2It's undefined, as $0^0$ is undefined. – Paul Jul 23 '19 at 19:57
-
See here: https://math.stackexchange.com/q/699740/471884 – ə̷̶̸͇̘̜́̍͗̂̄︣͟ Jul 23 '19 at 19:57
-
It's obviously the identity matrix, by definition. Powers with nonnegative exponent are defined by recursion: $A^0=I$, $A^{n+1}=A^nA$. No proof is needed for a definition. – egreg Jul 23 '19 at 20:06