11–20 of 54 posts
Yet to see a "Gentle Introduction to" that didn't freely and accurately translate to poorly written, impenetrable prose whose purpose is to gratify the ego of the author in demonstrating how they are unbelievably more clever than any reader who could conceivably require any kind of "introduction" Is that bad luck on my part? (I've given up on thinking I'm particularly or especially dense - while making no claims to b…
Yet to see a "Gentle Introduction to" that didn't freely and accurately translate to poorly written, impenetrable prose whose purpose is to gratify the ego of the author in demonstrating how they are unbelievably more clever than any reader who could conceivably require any kind of "introduction" Is that bad luck on my part? (I've given up on thinking I'm particularly or especially dense - while making no claims to b…
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 wh…
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 wh…
Could you recommend a text/paper/blog article which develops tensor theory from an algebraic setting?
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 wh…
Could you recommend a text/paper/blog article which develops tensor theory from an algebraic setting?
https://www.youtube.com/watch?v=4l-qzZOZt50
(You might get more mileage if you also watch the preceding lecture(s) of this excellent series.)
A tensor of rank N is a vector in a space whose basis is a set of N-tuples of ordinary vectors. That's it. So a rank-1 tensor is just a regular vector. A rank-2 tensor is a vector in a space whose basis is ordered pairs of regular vectors, a rank-3 tensor is a vector in a space whose basis is ordered triples of regular vectors, and so on.
He takes the more geometrical perspective as a tensor as a multi-linear function of vectors, from which all other statements about tensors (eg how the components transform) follows straightforwardly. Lots of other great material in this book and best of all there are loads of examples.