Determine if matrix is upper triangular
Create a 5-by-5 matrix.
A = triu(magic(5))
A = 17 24 1 8 15 0 5 7 14 16 0 0 13 20 22 0 0 0 21 3 0 0 0 0 9
Test A to see if it is upper triangular.
ans = 1
The result is logical 1 (true) because all elements below the main diagonal are zero.
Create a 5-by-5 matrix of zeros.
Z = zeros(5);
Test Z to see if it is upper triangular.
ans = 1
The result is logical 1 (true) because an upper triangular matrix can have any number of zeros on the main diagonal.
A matrix is upper triangular if all elements below the main diagonal are zero. Any number of the elements on the main diagonal can also be zero.
For example, the matrix
is upper triangular. A diagonal matrix is both upper and lower triangular.
Use the triu function to produce upper triangular matrices for which istriu 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, istriu(A) == isbanded(A,0,size(A,2)).