Calculating the dot product using non-orthonormal bases in a Euclidean space. This means that our metric tensor will have different elements than just 1's in the diagonal and 0's in the off-diagonal, but it still describes the same space, just using different basis vectors.
Lecture Notes: https://authortomharper.com/wp-conten...
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Other Resources
Youtube Playlists on Tensors
eigenchris
Tensors for Beginners: • Tensors for Beginners
Tensor Calculus: • Tensor Calculus
Relativity: • Relativity by eigenchris
Andrew Dotson
New to Tensors? • New To Tensors? Start Here
XylyXylyX
What is a Tensor? • What is a Tensor?
What is General Relativity? • What is General Relativity?
Books
A Student’s Guide to Vectors and Tensors by Daniel A. Fleisch
https://www.amazon.com/Students-Guide...
Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carroll
https://www.amazon.com/Spacetime-Geom...