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