# Diagonal of non-square matrix

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Shuqing Qi on 27 Apr 2021
Commented: Shuqing Qi on 27 Apr 2021
How can I build this matrix? All elements are zero except those three main diagonals. n is any given number.

Matt J on 27 Apr 2021
n=8;
R=[2,3,4,zeros(1,n+2-3)];
C=[2,zeros(1,n-1)];
T=toeplitz(C,R)
T = 8×10
2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4
Shuqing Qi on 27 Apr 2021
Thank you!

Bruno Luong on 27 Apr 2021
Edited: Bruno Luong on 27 Apr 2021
n = 8;
A = spdiags([2 3 4]+zeros(n,1),0:2,n,n+2);
A = full(A) % if prefered
A = 8×10
2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4 0 0 0 0 0 0 0 0 2 3 4
Shuqing Qi on 27 Apr 2021
Thank you!

Clayton Gotberg on 27 Apr 2021
Edited: Clayton Gotberg on 27 Apr 2021
n = 5; % Example input
diagonals = [2 3 4];
% Method 1:
matrix = zeros(n,n+2); % Preallocate for speed
extra_zeros = zeros(1,n-1);
matrix_row = [diagonals extra_zeros];
for k = 1:n
matrix(k,:) = matrix_row;
matrix_row = circshift(matrix_row,1);
end
% Method 2:
diagonal_one = [diag(repmat(diagonals(1),n,1)) zeros(n,2)];
diagonal_two = [zeros(n,1) diag(repmat(diagonals(2),n,1)) zeros(n,1)];
diagonal_three = [zeros(n,2) diag(repmat(diagonals(3),n,1))];
matrix = diagonal_one+diagonal_two+diagonal_three;
The second method is a little faster.
Shuqing Qi on 27 Apr 2021
Thank you!