I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ...(adsbygoogle = window.adsbygoogle || []).push({});

I am focused on Section 10.1 Introduction to Tensor Products ... ...

I need help with another aspect of the proof of Theorem 10.2 regarding the basis of a tensor product ... ...

Theorem 10.2 reads as follows:

A diagram involving the mappings [itex]\iota[/itex] and [itex]\gamma'[/itex] is as follows:

My questions are as follows:

Question 1

How do we know that there exists a multilinear map [itex]\gamma' \ : \ X \longrightarrow Z'[/itex] ?

Question 2

What happens (what are the 'mechanics') under the mapping [itex]\gamma'[/itex] ... ... to the elements in X\X' ( that is [itex]X - X'[/itex])? How can we be sure that these elements end up in [itex]Z'[/itex] and not in Z\Z'? (see Figure 1 above)

Hope someone can help ...

Peter

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# I Basis of a Tensor Product - Theorem 10.2 - Another Question

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