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Hadamard's Inequality

Let A=a_(ik) be an arbitrary n×n nonsingular matrix with real elements and determinant |A|, then

|A|^2<=product_(i=1)^n(sum_(k=1)^na_(ik)^2).

See also

Hadamard's Theorem

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References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1110, 2000.

Referenced on Wolfram|Alpha

Hadamard's Inequality

Cite this as:

Weisstein, Eric W. "Hadamard's Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HadamardsInequality.html

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