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Nondegenerate Bilinear Form


A bilinear form B:V×V->F on a finite-dimensional vector space is nondegenerate if

 B(v,w)=0 for all w in V

implies v=0, and likewise with the two arguments interchanged. Equivalently, the associated linear map V->V^* is an isomorphism. In a basis, this is equivalent to the matrix of B being a nonsingular matrix.


See also

Bilinear Form, Degenerate, Inner Product

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References

Roman, S. Advanced Linear Algebra, 3rd ed. New York: Springer, 2008.

Cite this as:

Weisstein, Eric W. "Nondegenerate Bilinear Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NondegenerateBilinearForm.html

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