I know this is an elementary question, however I am really lost as to where to start.  Since both $\mathbb{R}$ and $\mathbb{C}$ are finite-dimensional I think the inner product will be completely determined by the basis $\{1\}$.   I am not sure where to go from here.
This is a question of the book Linear Algebra of Kenneth Hoffman.  Describe explicitly all inner products on $\mathbb{R}$ and on $\mathbb{C}$.  I think that if $&lt;,&gt;$ is one inner product on $\mathbb{R}$ (or $\mathbb{C}$) then $&lt; ,&gt;=K[,]$, where $[,]$ is the standard inner product. Is that correct?
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