Check whether every entry above the main diagonal of a square matrix is zero.
How It Works
How Lower Triangular Matrix Checker Works
The calculator checks every position strictly above the main diagonal (where the column index is greater than the row index) and confirms each one is zero — entries on or below the diagonal can be anything.
Worked Example
See It In Action
The matrix with rows 1,0,0 / 2,3,0 / 4,5,6 is lower triangular since every entry above the diagonal is 0.
FAQ
Frequently Asked Questions
What's the practical benefit of a matrix being lower triangular?
Systems of equations with a lower triangular coefficient matrix can be solved directly by forward substitution, one variable at a time, without the extra work a general system requires — this is a core building block of LU decomposition, used to solve much larger linear systems efficiently.
What's the determinant of a lower triangular matrix?
It's simply the product of the entries on the main diagonal — a handy shortcut over the full cofactor expansion needed for a general matrix.
