$$ L(R,R;R)=\{f:R\times R\rightarrow R : f \text{ is bilinear } \} $$ Adding the addition and scalar product, $L(R,R;R)$ is a vector space .
How to show $L(R,R;R)\cong R$ ? Besides what is the basis of $L(R,R;R)$ ?
2026-03-28 23:58:40.1774742320
How to show $L(R,R;R)\cong R$?
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Hint: let $f\colon R\times R\to R$ be a bilinear map. Then, for $(x,y)\in R\times R$ you have $$ f(x,y)=xyf(1,1) $$