I am reading Segei Winitzki's book: Linear Algebra via Exterior Products ...(adsbygoogle = window.adsbygoogle || []).push({});

I am currently focused on Section 1.7.3 Dimension of a Tensor Product is the Product of the Dimensions ... ...

I need help in order to get a clear understanding of an aspect of the proof of Lemma 3 in Section 1.7.3 ...

The relevant part of Winitzki's text reads as follows:

In the above quotation from Winitzki we read the following:

" ... ... By the result of Exercise 1 in Sec. 6.3 there exists a covector [itex]f^* \in V^*[/itex] such that

[itex]f^* ( v_j ) = \delta_{ j_1 j }[/itex] for [itex]j = 1, \ ... \ ... \ , \ n[/itex] ... ... "

I cannot see how to show that there exists a covector [itex]f^* \in V^*[/itex] such that

[itex]f^* ( v_j ) = \delta_{ j_1 j }[/itex] for [itex]j = 1, \ ... \ ... \ , \ n[/itex] ... ...

Can someone help me to show this from first principles ... ?

It may be irrelevant to my problem ... but I cannot see the relevance of Exercise 1 in Section 6 which reads as follows:

Exercise 1 refers to Example 2 which reads as follows:

BUT ... since I wish to show the result:

... ... ... "there exists a covector [itex]f^* \in V^*[/itex] such that

[itex]f^* ( v_j ) = \delta_{ j_1 j }[/itex] for [itex]j = 1, \ ... \ ... \ , \ n[/itex] ... ..."

...the above example is irrelevant ... BUT then ... I cannot see its relevance anyway!!!from first principles

Hope someone can help ... ...

Peter

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*** NOTE ***

To help readers understand Winitzki's approach and notation for tensors I am providing Winitzki's introduction to Section 1.7 ... ... as follows ... ... :

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# I Tensors - Winitzki - Lemma 3

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