@MatheiBoulomenos: Googling led me to this paper. Have you seen it? algant.eu/documents/theses/simachew.pdf ... I don't know if it answers your specific question.
Let $P = \{2, 3, 5, \dots \}$ be the primes and $S_P$ be the set of all their permutations.
Let $f(X,Y,Z) = f(\bar{X})$ be the polynomial form say $f = XY + Z$. Define $\phi \in S_P$ to be a polynomial automorphism of primes asscociated with $f$ if $\phi$ commutes with $f$ at all primes:
$$
a,...
Each year a tree grows 5 centimetre less than that it did the preceding year if it grew by 1 metre in the first year in how many years will it have ceased growing?
For $ 0 \leq x $ ,
Find Pairs of analytic functions $f,g$ such that
$$f(x+1) = 2 f(x)^2 + 3 g(x)^2 + 4 f(x) + 5 g(x) + 6$$
$$g(x+1) = f(x)^2 + 7 g(x)^2 + 8 f(x) + 9 g(x) + 10$$
hold simultanously.
I know some stuff about complex dynamics and I know people who know alot more than me about it....
@MeowMix, @Hippalectryon one can think of a matrix as a discrete function of the indices over some range. So the natural thing to think is what would happen if it went from integer indices to real number indices. I can think of how to represent matrix addition and multiplication. I just cannot seem to determine how the determinant would work. I think it would have something to do with real powers of -1... but I'm not 100% sure.
im wondering if it might be relevant to analysis in some way. For instance, if the determinant were a familiar looking function then we might be able to use linear algebra theorems to prove complicated analytical statements.
(or at least expand discrete linear algebra into a real linear algebra)
Let $P = \{2, 3, 5, \dots \}$ be the primes and $S_P$ be the set of all their permutations.
Let $f(X,Y,Z) = f(\bar{X})$ be the polynomial form say $f = XY + Z$. Define $\phi \in S_P$ to be a polynomial automorphism of primes asscociated with $f$ if $\phi$ commutes with $f$ at all primes:
$$
a,...
Each year a tree grows 5 centimetre less than that it did the preceding year if it grew by 1 metre in the first year in how many years will it have ceased growing?
For $ 0 \leq x $ ,
Find Pairs of analytic functions $f,g$ such that
$$f(x+1) = 2 f(x)^2 + 3 g(x)^2 + 4 f(x) + 5 g(x) + 6$$
$$g(x+1) = f(x)^2 + 7 g(x)^2 + 8 f(x) + 9 g(x) + 10$$
hold simultanously.
I know some stuff about complex dynamics and I know people who know alot more than me about it....
