# Question:Generate a matrix and block matrix

## Question:Generate a matrix and block matrix

Maple 2015

Dear Users!

Hoped everyone fine with everything. I the following maple expression, I need a matrix A for each n. Like if I take k =1 I want A[1]; if I take k=2, I want A[1], A[2]; for k=3 I want A[1], A[2], A[3] and so on. A[i]'s is square matrix having order M-1 by M-1.

Further I want to generate a block matrix for k. Like for k=1 I want a block matrix as Vector(1, {(1) = A[1]}), for k=2 I want a block matrix as Matrix(2, 2, {(1, 1) = A[1], (1, 2) = 0, (2, 1) = 0, (2, 2) = A[2]}), for k =3 I want a block matrix as Matrix(3, 3, {(1, 1) = A[1], (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = A[2], (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = A[3]}) and so on.

restart; alpha := 1;
k := 2; M := 3;
printlevel := 3;

for n while n <= 2^(k-1) do

for m from 0 while m <= M-1 do

for j from 0 while j <= M-1 do

Omega[m, j] := 2^((1/2)*k)*sqrt(GAMMA(j+1)*(j+alpha)*GAMMA(alpha)^2/(Pi*2^(1-2*alpha)*GAMMA(j+2*alpha)))*(sum((-1)^i*GAMMA(j-i+alpha)*2^(j-2*i)*(sum((1/2)*binomial(m, l)*(2*n-1)^(m-l)*(1+(-1)^(j-2*i+l))*GAMMA((1/2)*j-i+(1/2)*l+1/2)*GAMMA(alpha+1/2)/GAMMA(alpha+1+(1/2)*j-i+(1/2)*l), l = 0 .. m))/(GAMMA(alpha)*factorial(i)*factorial(j-2*i)), i = 0 .. floor((1/2)*j)))/2^(k*(m+1))

end do

end do;

A[n]:=???

end do;

I am waiting for your positive response.

Thanks

﻿