Creating Diagonal Matrix from a Vector

I have a vector g = [g0 g1 g2 g3 ... gx]

I want to create a matrix of the form:

Here x = (m-n)

Any thoughts on how I can do this?

Answer 1

[Stephen23]

The efficient MATLAB approach:

g = [1,2,3,4,5];
z = zeros(1,numel(g)-1);
m = toeplitz([g(1),z],[g,z])

m = 5×9

1 2 3 4 5 0 0 0 0 0 1 2 3 4 5 0 0 0 0 0 1 2 3 4 5 0 0 0 0 0 1 2 3 4 5 0 0 0 0 0 1 2 3 4 5

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Answer 2

[Ameer Hamza]

This is one way

g = [1 2 3 4 5];
n = numel(g);

M_ = [eye(n) zeros(n,n-1)];
M = zeros(n, 2*n-1);
for i = 1:n
    M = M + circshift(M_*g(i), i-1, 2);
end

Result

>> M
M =
     1     2     3     4     5     0     0     0     0
     0     1     2     3     4     5     0     0     0
     0     0     1     2     3     4     5     0     0
     0     0     0     1     2     3     4     5     0
     0     0     0     0     1     2     3     4     5

Answer 3

[Bruno Luong]

>> g=[1 2 3]

g =

     1     2     3

>> p=length(g);
>> s=10;
>> A=full(spdiags(repmat(g,s,1),0:p-1,s,s+p-1))

A =

     1     2     3     0     0     0     0     0     0     0     0     0
     0     1     2     3     0     0     0     0     0     0     0     0
     0     0     1     2     3     0     0     0     0     0     0     0
     0     0     0     1     2     3     0     0     0     0     0     0
     0     0     0     0     1     2     3     0     0     0     0     0
     0     0     0     0     0     1     2     3     0     0     0     0
     0     0     0     0     0     0     1     2     3     0     0     0
     0     0     0     0     0     0     0     1     2     3     0     0
     0     0     0     0     0     0     0     0     1     2     3     0
     0     0     0     0     0     0     0     0     0     1     2     3

     % This work as well
>> A = toeplitz([g(1) zeros(1,s-1)],[g zeros(1,s-1)]);

Answer 4

[KSSV]

g = rand(1,4) ; 
m = length(g) ; 
P  =zeros(m) ;

d=size(diag(P,i),1);%this is the size of the vector with elements of the kth diagonal
for i = 1:m
  e=g(i)*ones(m+1-i,1);
  P = P+diag(e,i-1);
end