M is a 2 x 2 matrix with each of the 4 elements being real. Can there exist an integer G ≥ 2, for which the following relationship is satisfied?
[0 1]
M^{G} = 
[0 0]
If the answer to the above question is "no", prove it. Otherwise, cite an appropriate example.
Determinants?
Been a long time! Charlie slipped this one in while I was playing around with this in Excel on another computer.
Haven't got a solution but re the format, ⌈ ⌉ ⌊ and ⌋ might be worthy considerations should such a format be needed in the future (works in my editor, unsure about Perplexus).
Solutionwise, I begin with a matrix:
0 0 and arrive at 0 0 and 0 0
0 1 by squaring 0 1 by cubing 0 1.
Since the latter matrix is a 90º rotation of what is sought I have a sense that our initial matrix is something like my initial one, not necessarily in that array, but also raised to yet a higher power.
Playing with this further, and raising the power to 4 just seems to create a kind of flipflop mirroring but sometimes with diagonally values being signed differently.
At the moment this appears to beg a proof to prove such a G may not exist.
Edited on June 20, 2009, 12:15 pm

Posted by brianjn
on 20090620 11:46:49 