 Analytic matrices and the base units - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Analytic matrices and the base units (/showthread.php?tid=1176) Analytic matrices and the base units - Xorter - 07/18/2017 Hi, there! I have been looking for the number of the dimensions of the hyper- and interdimensional spaces of the Multiverse for long years. This is why my last thread about the Taylor series of i[x] is. I guess the next step is to create analytic matrices in where between two value there is another one. Because we can check the existence of the hyper- and interdimensional spaces by matrix-multiplication, cannot we? Here is an example: Let  F = [ f(x,y) ] and G = [ g(x,y) ] be  so-called functional or analytic matrices. My question is that what are F*G, F^n, F^-1, |F| (determinant) ? I suppose that F+G = [ f(x,y)+g(x,y) ] I think this way leads us to the solutuion of the dimension-question. Any idea? RE: Analytic matrices - Xorter - 07/18/2017 Ah, yes, I forgot something to write: F_{i j} = f(i,j) And another question: Are these are related to Carleman matrices? RE: Analytic matrices - Xorter - 07/19/2017 I have found something: https://math.stackexchange.com/questions/2024034/matrices-with-continuous-indices Would it be the solution for multiplication functional / analytic matrices? So F*G = [ f(x,y) ]*[ g(x,y) ] = [ int from alpha to beta f(x,u)*g(u,y) du ] But I have a question: Why does not it work with constants?! The next question: what is the analytic representation of the imaginary base units? We can be sure that: [ 1 ] = [ x, 0; 0, x ]^oinfinity o 1, but what is i? Could it be [ i ] = [ x, 0; 0, x ]^oinfinity o [ 0, 1; -1, 0 ] ? And what is about the interdimensional base units, like i[1.5]? I feel we are closer than ever before.