What's a Tensor?
Why Physics Stack Exchange recommends it
Physics Stack Exchange users link it as an intuitive, maths-light answer to the question of what a tensor actually is, and as a source for the idea that observers agree on the combination of components and basis vectors.
Recommended by 2 people across 2 different months, 2013 to 2020.
What it is
Dan Fleisch, author of A Student's Guide to Vectors and Tensors, gives a short visual introduction to what tensors are. He builds up from vectors and basis vectors to second-rank tensors, using simple physical props like blocks, arrows and cardboard rather than heavy formalism.
What people said
Recommends Peter4075 · 2013-08 · Physics Stack Exchange · on “Understanding Tensors”
You could probably do a lot worse than taking a look at the video "What's a Tensor?" by Daniel Fleische on YouTube: [this video] He gives a nicely visual, but maths-lite answer to that question by using children's blocks, small arrows, a couple of pieces of cardboard and a pointed stick.
Recommends NaiveBayesian · 2017-06 · Physics Stack Exchange · on “Metric Tensor as the Simplest Mathematical Object that can Define a Space (or Spacetime)”
I've been reading Fleisch's " A Student's Guide to Vectors and Tensors [LINK] " as a self-study, and watched this helpful video [this video] , also by Fleisch. Suddenly co-vectors and one-forms make more sense than they did when I tried to learn the from Schutz's GR book many years ago. Especially in the video, Fleisch describes one way of viewing a second-rank tensor; as an object whose individual components relate the input and output components of two sets basis vectors. In Chapter 4 of his book, Fleisch draws careful attention to two different ways that second rank tensors can be used to relate vectors; they can be used to change a vector, or to change the coordinate representation of a vecto
Cites Physiks lover · 2016-04 · Physics Stack Exchange · on “What's meant by: "All observers agree on the combination of basis vectors and components for a tensor"?”
There's a [this video] given by Dr Dan Fleisch on Tensors, where he states at 11:22: You may be wondering, what is it about the combination of components and basis vectors that makes tensors so powerful? The answer is this: All observers in all reference frames agree, not on the basis vectors, not on the components, but upon the combination of components and basis vectors " What does he mean? Is he saying that as you change the combination of basis vectors, you also change the corresponding components?
Cites PNS · 2020-05 · Physics Stack Exchange · on “Why is mass an invariant in Special Relativity?”
Introduction: In Special Relativity, when we say a quantity is an invariant, we mean that it is a Lorentz invariant. What this means is that when you apply the Lorentz transforms [LINK] to any frame of reference, the magnitude of the Lorentz invariant does not change. The Lorentz invariant is a scalar, which means that it can only have a magnitude, and can carry no other information. Instead, if we take something like a vector (something which has magnitude but also contains information about direction), then the magnitude would still be the same, but the information about the direction changes, so it could not be an invariant. Also, in Special Relativity we say that events occur in 'spaceti