MATLAB: How to create a matrix with 1 on ij-th position and zeros elsewhere from a lower triangular matrix

matrix algebra

It may be a very simple question For a symmetric matrix A (3×3), say A=[2 4 6;4 8 11;6 11 20], the way to extract its unique elements (on and lower the diagonal) in an output vector B is:
B=(A(tril(A)~=0))
B =  2
     4
     6
     8
    11
    20
How can I create matrices C1,C2,C3,…,C6, such that
B(1)=A.*C1, B(2)=A.*C2, ..., B(6)=A.*C6
C1=[1 0 0;0 0 0;0 0 0];
C2=[0 0 0;1 0 0;0 0 0];
C3=[0 0 0;0 0 0;1 0 0];
C4=[0 0 0;0 1 0;0 0 0];
C5=[0 0 0;0 0 0;0 1 0];
C6=[0 0 0;0 0 0;0 0 1];

Best Answer

A = [2,4,6;4,8,11;6,11,20] 
S = size(A);
T = tril(true(S));
[R,C] = find(T);
N = nnz(T);
Z = zeros([S,N]);
V = 1:N;
Z(sub2ind([S,N],R,C,V(:))) = 1
Each page of Z (i.e. the third dimension) is one of the requested matrices, which you can access easily using indexing:
>> Z(:,:,1)
ans =
   1   0   0
   0   0   0
   0   0   0
>> Z(:,:,2)
ans =
   0   0   0
   1   0   0
   0   0   0
...
>> Z(:,:,6)
ans =
   0   0   0
   0   0   0
   0   0   1
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