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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

\begin{displaymath}
{\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].
\end{displaymath}

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.




© 1996-9 Eric W. Weisstein
1999-05-26