[HN Gopher] A Gentle Introduction to Tensors (2014) [pdf] ___________________________________________________________________ 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 ___________________________________________________________________ (page generated 2021-08-17 23:00 UTC)