= Perfect pairing
{title2=$B:V\times W\to F$}
For finite-dimensional <vector spaces> $V,W$ over a <field> $F$, a bilinear pairing $B:V\times W\to F$ is perfect when the induced <linear maps> $V\to W^*$ and $W\to V^*$ are <isomorphisms>. Equivalently, both dimensions agree and the matrix of the pairing in any two bases is invertible. The evaluation pairing between a finite-dimensional <vector space> and its <dual space> is perfect. This notion allows two different spaces; a <nondegenerate bilinear form> is the case $V=W$.
Back to article page
