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GeezerVison is showing mathworld.wolfram.com — Minimal Matrix -- from Wolfram MathWorld

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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

M=[1 -1 0 0; 0 0 -1 0; 1 1 1 -1; 0 0 1 0].

There are 2^(n-1) minimal special matrices of size n×n.

See also

Special Matrix

Explore with Wolfram|Alpha

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More things to try:

  • alternating group A_5
  • Gamma(11/2)
  • interpolating polynomial calculator

References

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

Referenced on Wolfram|Alpha

Minimal Matrix

Cite this as:

Weisstein, Eric W. "Minimal Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MinimalMatrix.html

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