Link: What is a tensor? (vimeo.com)

2 · 3 comments delete · by kalid 2 years ago

Great vid explaining the essence of a tensor -- matching up components with basis vectors.

Rank 0 (scalar) : component, but no basis vectors Rank 1 (vector) : component & 1 basis vector (1 x 3) Rank 2 (array) : component matched with 2 basis vectors. (3x3)

(1 basis vector could be direction of surface, the other is the force applied in the x-direction).

Key useful property (which I need to understand): the combination of components & basis vectors can be agreed-upon by all reference frames (moving, rotating, etc.). What does the "combination" refer to? ("Coordinate-free" -- express relationship between vectors). More on coordinate-free geometry: http://www.cs.brown.edu/~ls/teaching08/LN04_Coordfreegeom.pdf

No absolute coordinates -- you just have a "point" and a vector (with direction and magnitude). But it's not on some grid with x and y components. Coordinates are needed to implement, but not reason about, the coordinate system.

Comments

  1. The guy in the video also wrote a book I'm reading at the moment (http://www.amazon.co.uk/Students-Guide-Maxwells-Equations/dp/0521701473) which is also full of intuitive explanations

    Greg - about 2 years ago
  2. Awesome, thanks for the pointer! Looking forward to checking it out.

    Thanks for the suggestion too -- you can enter LaTeX equations between double dollar signs:

       
    $$x^2 + y^2 = z^2$$

    $$x^2 + y^2 = z^2$$

    kalid - about 2 years ago
  3. Smashing, thanks & keep up the fantastic work.

    - about 2 years ago

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