An upper triangular matrix is a square matrix for which every value below the diagonal must be 0. That is to say:
[ a1,1 a1,2 a1,3 ... a1,n ]
[ 0 a2,2 a2,3 ... a2,n ]
A = [ 0 0 a3,3 ... a3,n ]
[ ... ... ... ... ... ]
[ 0 0 0 ... an,n ]
Also defined is the strictly upper triangular matrix for which values on the diagonal must also be 0:
[ 0 a1,2 a1,3 ... a1,n ]
[ 0 0 a2,3 ... a2,n ]
A = [ 0 0 0 ... a3,n ]
[ ... ... ... ... ... ]
[ 0 0 0 ... 0 ]
A more formal definition for the standard upper triangular matrix would be
ai,j =
{ 0, i > j
{ ai,j, i ≤ j
And for the strictly upper triangular matrix:
ai,j =
{ 0, i ≥ j
{ ai,j, i < j
Also see: