What is a Tensor

This Youtube reproduction list is a fantastic place to understand what is a Tensor.

It goes all the way to explain how tensors are defined. It starts from vectors, linear maps, dual spaces, tensor product and finally they arrive to the definition of tensors.

Very clear!!

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Tensor analysis and introduction to tensors

This is an incredible series of lectures from Pavel Grinfeld:

and here is a whole series of lectures on linear algebra and tensor calculus from the same professor that is extraordinarily good

https://www.youtube.com/channel/UCr22xikWUK2yUW4YxOKXclQ/playlists

His is also this book:

http://www.amazon.es/Introduction-Tensor-Analysis-Calculus-Surfaces/dp/1461478669

Tensors, Metric Tensors

If you want to learn about tensors and metric tensors , read:

http://www.drchristiansalas.org.uk/MathsandPhysics/Relativity/Gravitation.pdf    …..chapter 2

http://www.amazon.es/Gravitation-Physics-Series-Charles-Misner/dp/0716703440

https://1e47a410-a-62cb3a1a-s-sites.googlegroups.com/site/winitzki/linalg/Linear_algebra_exterior.pdf?attachauth=ANoY7crfG0SKhDzy0qTo6tge1w_1jcqGvWTtVH7Ljw6qxoySN6TSNwmfeYl1z7qlcfWL244Hq2D3dug_mUpPpVF-gUKE4Fa-Eix2FOIPAcFH7-EcAB6fZbReuQWRtNZ3WMtWvvo5sdh9dXbSuUNr130i2W2wdjhO7WTo_8OYQCYyrKvhPdRWBgXvbHUhVxuO04luLJMd06iBwkJAgN_VJxPTAxAR_mrbR6P29wIIKIyG-bOmQf_KExs%3D&attredirects=0

This is a very good introduction….