 Quote by mathwonk
tensors are combinations of vectors and functions on vectors. contracting means you have one of each type and you evaluate the function on the vector (or multivector).
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You mean linear functions on vectors - and those I prefer to call forms.
And please don't talk about contraction before you define what a tensor is... Because if you do (and people do) than everything related to tensors shrinks to manupulation of components...
And still I find your description somehow inaccurate: you should specify what does your vectors mean in every single place in your statement. (e.g. [tex]\alpha \in V^*[/tex] is one-form on [tex]V[/tex] but vector in [tex]V^*[/tex])