Minimal Matrix

A Matrix with 0 Determinant whose Determinant becomes Nonzero when any element on or below the diagonal is changed from 0 to 1. An example is

$${\hbox{\sf M}}=\left[{\matrix{1 & -1 & 0 & 0\cr 0 & 0 & -1 & 0\cr 1 & 1 & 1 & -1\cr 0 & 0 & 1 & 0\cr}}\right].$$

There are $2^n-1$ minimal Special Matrices of size $n\times n$.

See also Special Matrix

References

Knuth, D. E. ``Problem 10470.'' Amer. Math. Monthly 102, 655, 1995.