About Vectors (Banesh Hoffmann) pdf, epub, doc

About Vectors ePub and PDF Available
Here is how this book ends.Quite a thrilling conclusion if you ask me!

10. WHAT THEN IS A VECTOR?

This being a book about vectors, we have presented only the sketchiest account of tensors— barely enough to illustrate the advantages of thinking of vectors in terms of the way their components transform.

We have one final point to make.Notice that we defined contravariant vectors and covariant vectors— indeed, tensors of all ranks—before we introduced the metrical tensor.Suppose there were no metrical tensor.What could we then say about the magnitudes of vectors?Or about the cosines of the angles between them?

You may be tempted to argue that such questions prove that there has to be a metrical tensor.But actually there does not.Mathematicians often work with spaces that do not possess one; they call them nonmetrical spaces.

Thus vectors do not have to have magnitudes.And this is as good a place as any to stop.

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Book info

  • Author:
  • Publisher:Dover Publications
  • File: 5.7 Mb
  • Ganre: Science
  • Release: 01.06.1975
  • ISBN: 9780486604893
  • Pages 144
  • Rating: 4.46 (17 votes)

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