Dual Spaces .... Friedberg et al, Example 4, Section 2.6

  • #1
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I am reading the book: "Linear Algebra" by Stephen Friedberg, Arnold Insel, and Lawrence Spence ... and am currently focused on Section 2.6: Dual Spaces ... ...

I need help with an aspect of Example 4, Section 2.6 ...

Example 4, Section 2.6 reads as follows: (see below for details of Section 2.6 ...)View attachment 8743Can someone please explain (in detail) how/why ... ?

Help will be appreciated ...

Peter
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To understand the context and notation of the above example it may help MHB readers to have access to the text of Section 2.6 ... so I am providing the same ... as follows ...
View attachment 8744
View attachment 8745
Hope that helps ...

Peter
 

Attachments

  • FIS - Example 4, Section 2.6 ... .png
    FIS - Example 4, Section 2.6 ... .png
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  • FIS - 1 - Section 2.6 Dual Spaces ... PART 1 ... .png
    FIS - 1 - Section 2.6 Dual Spaces ... PART 1 ... .png
    42.8 KB · Views: 87
  • FIS - 2 - Section 2.6 Dual Spaces ... PART 2 ... .png
    FIS - 2 - Section 2.6 Dual Spaces ... PART 2 ... .png
    37.7 KB · Views: 98
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  • #2
Peter said:
Can someone please explain (in detail) how/why ... ?
This comes directly from the definition of the dual basis. In Example 3 of Section 2.6, Friedberg, Insel and Spence say "Note that , where is the Kronecker delta." In this example, the first element of the given basis is . So
 
  • #3
Opalg said:
This comes directly from the definition of the dual basis. In Example 3 of Section 2.6, Friedberg, Insel and Spence say "Note that , where is the Kronecker delta." In this example, the first element of the given basis is . So
Thanks Opalg ...

Appreciate your help...

Peter
 
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