Determine if matrix is lower triangular
Create a 5-by-5 matrix.
D = tril(magic(5))
D = 17 0 0 0 0 23 5 0 0 0 4 6 13 0 0 10 12 19 21 0 11 18 25 2 9
Test D to see if it is lower triangular.
ans = 1
The result is logical 1 (true) because all elements above the main diagonal are zero.
Create a 5-by-5 matrix of zeros.
Z = zeros(5);
Test Z to see if it is lower triangular.
ans = 1
The result is logical 1 (true) because a lower triangular matrix can have any number of zeros on its main diagonal.
A matrix is lower triangular if all elements above the main diagonal are zero. Any number of the elements on the main diagonal can also be zero.
For example, the matrix
is lower triangular. A diagonal matrix is both upper and lower triangular.
Use the tril function to produce lower triangular matrices for which istril returns logical 1 (true).
The functions isdiag, istriu, and istril are special cases of the function isbanded, which can perform all of the same tests with suitably defined upper and lower bandwidths. For example, istril(A) == isbanded(A,size(A,1),0).