Link: What is a tensor? (

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:

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.


  1. The guy in the video also wrote a book I'm reading at the moment ( 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

Add Comment

Share the insights that worked

Let's find the aha! moments that helped ideas click.

We'll organize the best into intuitive introductions to a topic.

The site is in beta and