How to build a growing square matrix with the following values?

I am working on some code to find the condition of a spring matrix. I know the matrix in question, but I am not sure how to create a for-loop to make a bigger matrix after every iteration. In general, the matrix looks something this:

Considering the simple case where k1=k2=kn=1.

How would I go about constructing this matrix, computing a condition, then constructing a bigger matrix, computing the condition, and so on?

Answer 1

[Akira Agata]

I think this code will generate the matrix.

n = 10;
k = ones(n+1,1);

for kk = 1:n
  A = - diag(k(1:kk)) - diag(k(2:kk+1));
  if kk>1
      A = A + diag(k(2:kk),-1) + diag(k(2:kk),1);
  end
  % To display the matrix for each loop
  A
end

The value k_1 ~ k_n in your picture corresponds to the array k in this script.

[Ibro Tutic]

Thanks for the help!