Add a diagonal of zeros to a matrix in MATLAB

Question

Suppose I have a matrix A of dimension Nx(N-1) in MATLAB, e.g.

N=5;
A=[1  2  3  4;
   5  6  7  8;
   9  10 11 12;
   13 14 15 16;
          


        

Answer 1

If you want to insert any vector on a diagonal of a matrix, one can use plain indexing. The following snippet gives you the indices of the desired diagonal, given the size of the square matrix n (matrix is n by n), and the number of the diagonal k, where k=0 corresponds to the main diagonal, positive numbers of k to upper diagonals and negative numbers of k to lower diagonals. ixd finally gives you the 2D indices.

function [idx] = diagidx(n,k)
% n size of square matrix
% k number of diagonal
if k==0 % identity
    idx = [(1:n).' (1:n).']; % [row col]
elseif k>0 % Upper diagonal
    idx = [(1:n-k).' (1+k:n).'];
elseif k<0 % lower diagonal
    idx = [(1+abs(k):n).' (1:n-abs(k)).'];
end
end

Usage:

n=10;
k=3;
A = rand(n);
idx = diagidx(n,k);

A(idx) = 1:(n-k);