Matrix With Produnct


Kx1 = 1.75; n = 10; \[Theta]1 = 0; \[Theta]2 = \[Pi] / 2; rmax =  2 \[Pi]; nr = 10; 

fxy[[Theta], r] := N[{Mod[[Theta] + r – Kx1 Sin[[Theta]], 2 [Pi], -[Pi]], Mod[r – Kx1 Sin[[Theta]], 2 [Pi], -[Pi]]}];

MapData1 = Flatten[Table[Join[NestList[fxy @@ # &, {[Theta]1, i rmax / nr}, n], NestList[fxy @@ # &, {[Theta]2, i rmax / nr}, n]], {i, 0, nr}], 1];

[Chi]1 = -1/2 Sqrt[(2 MapData1[[All, 2]])/(.2)] Cos[MapData1[[All, 1]]];

[Zeta] = -1/2 0.2 10;

K1 = Sin[[Zeta]] Cot[[Chi]1];

[Eta][n_] = 1/(Sqrt[2] Sqrt[Sqrt[1 + K1^2]] Sqrt[Sqrt[1 + K1^2] + K1]);

[Xi][n_] = (Sqrt[1 + K1^2] + K1)/(Sqrt[2] Sqrt[Sqrt[1 + K1^2]] Sqrt[ Sqrt[1 + K1^2] + K1]);

[Phi]1 = ArcCos[Cos[Cos[[Chi]1] Cos[[Zeta]]]];

A11[n_] = Exp[-I [Phi]1] ( [Eta][n] [Eta][n – 1] + [Xi][n] [Xi][n – 1]);

A12[n_] = Exp[-I [Phi]1] ( [Eta][n] [Xi][n – 1] – [Xi][n] [Eta][n – 1]);

A21[n_] = Exp[I [Phi]1] (- [Eta][n] [Xi][n – 1] + [Xi][n] [Eta][n – 1]);

A22[n_] = Exp[I [Phi]1] ( [Eta][n] [Eta][n – 1] + [Xi][n] [Xi][n – 1]);

Matrix[n_] = {{A11, A12}, {A21, A22}};

bigN = 100;

matrices = Map[matrix, Range[bigN]];

Apply[Dot, matrices]