- #1
yifli
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natural isomorphism from V to V**
It is known that there is a natural isomorphism [tex]\epsilon \rightleftharpoons \omega^\epsilon[/tex] from V to V**, where [tex]\omega: V \times V* \rightarrow R[/tex] is a bilinear mapping.
So given a certain [tex]\epsilon \in V[/tex], its image under the isomorphism is actually a set of values [tex]\left\{f(\epsilon),f \in V^*\right\}[/tex], i.e., a vector is mapped to a set of numbers
Is my understanding correct?
Thanks
It is known that there is a natural isomorphism [tex]\epsilon \rightleftharpoons \omega^\epsilon[/tex] from V to V**, where [tex]\omega: V \times V* \rightarrow R[/tex] is a bilinear mapping.
So given a certain [tex]\epsilon \in V[/tex], its image under the isomorphism is actually a set of values [tex]\left\{f(\epsilon),f \in V^*\right\}[/tex], i.e., a vector is mapped to a set of numbers
Is my understanding correct?
Thanks