Check whether a square matrix has zero entries everywhere beyond the first diagonal above the main diagonal.
How It Works
How Lower Hessenberg Matrix Checker Works
A looser version of lower triangular — instead of requiring everything above the main diagonal to be zero, it only requires everything beyond the first superdiagonal to be zero, so one extra non-zero band above the diagonal is allowed.
FAQ
Frequently Asked Questions
Why does this "almost triangular" form matter?
Hessenberg form is a standard intermediate step used to speed up eigenvalue algorithms — reducing a general matrix to Hessenberg form first makes the iterative methods that follow considerably faster to compute.
Is every lower triangular matrix automatically lower Hessenberg?
Yes — lower triangular is a stricter condition (nothing above the diagonal at all), so it automatically satisfies the looser lower Hessenberg requirement too.
