[HN Gopher] A Gentle Introduction to Tensors (2014) [pdf]
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       A Gentle Introduction to Tensors (2014) [pdf]
        
       Author : michaelsbradley
       Score  : 17 points
       Date   : 2021-08-17 21:42 UTC (1 hours ago)
        
 (HTM) web link (www.ese.wustl.edu)
 (TXT) w3m dump (www.ese.wustl.edu)
        
       | [deleted]
        
       | gerdesj wrote:
       | The author is clearly more comfortable with deploying beautifully
       | laid out mathematics than prose. The introduction or "Opening
       | Remarks" is lovely and well written but is nearly a wall of text.
       | There is one long first paragraph followed by some staccato
       | afterthoughts.
       | 
       | The author wavers between I and we. Am I your friend, guiding you
       | through the maze or are we lecturing you on something? The author
       | needs to settle on either one identity or spell out when they
       | become one or another.
       | 
       | Sometimes, you might wish to appear as a friend hovering over the
       | shoulder and provide hints as to the right direction to follow
       | and at other times you might deploy something that will give
       | LaTeX a headache and pull out the Vox Dei stop on the 250 ton
       | Organ and destroy nearby eardrums.
       | 
       | I love the paper and it is saved locally.
        
       | Koshkin wrote:
       | I have always hated when tensors are defined as something whose
       | coordinates are transformed in a certain way. I just find it
       | inherently unfriendly and un-geometric. No matter how much talk
       | is given about simpler cases such as scalars, vectors, covectors,
       | etc., the final defining formula would still look to me as
       | daunting as always. (There is nothing "gentle" about the formulas
       | on page 14.) Surprisingly or not, the whole thing clicked for me
       | when I eventually learned about tensors in a more abstract
       | algebraic setting, where they are defined as multilinear forms.
       | The coordinate transformation laws were very easy to understand
       | and remember after that.
       | 
       | But if you want to learn about tensors from how their coordinates
       | transform, here's a treat:
       | 
       | https://www.youtube.com/watch?v=CliW7kSxxWU
        
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       (page generated 2021-08-17 23:00 UTC)