I'm reading Lee's Introduction to Smooth Manifolds and I have a question on the definition of a multilinear function(adsbygoogle = window.adsbygoogle || []).push({});

Suppose [itex] V_{1},...,V_{k}[/itex] and [itex]W[/itex] are vector spaces. A map [itex] F:V_{1} \times ... \times V_{k} \rightarrow W [/itex] is said to be multilinear if it is linear as a function of each variable separately when the others are held fixed: for each i,

[itex] F(v_{1},...,av_{i} + a'v^{'}_{i},...,v_{k}) = aF(v_{1},...,v_{i},...,v_{k}) + a'F(v_{1},..., v^{'}_{i},...,v_{k}) [/itex]

I'm thinking that it should look like this,

[itex] F(u_{1},...au_{k} + a'v_{1},...,v_{k}) = aF(u_{1},...,u_{k})+a'F(v_{1},...,v_{k}) [/itex]

any comments?

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# Multilinear Algebra Definition

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