Where can I find some good resources on tensors?...

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Where can I find some good resources on tensors? I studied them few years ago in fluid mechanics and continuum medium mechanics but I forgot almost everything.

>I just remember that a tensor is to a vector what vectors are to scalars

>I remember the teacher repeating over and over that TENSORS ARE NOT MATRICES !!!

I since then graduated from a master in motion control where I hadn't had the occasion to manipulate tensors.

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We could meet up and form a study group

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>>7784940

Why would i do that? At best i might try to wrestle in some cheese whiz after smooth manifold calculations.

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>>7784942

>cheese whiz

Alright, I'm in. The only issue is, I'm British.

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>>7784943

Np, I'll visit, I already had your IP traced.

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What about tensors resources tho.

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>>7784947

But I'm posting through a VPN...

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>>7784955

Then enjoy your vpn getting banned.

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You start with two vector spaces [math] V [/math] and [math] W [/math] over the same field [math] \mathbb{K} [/math].

Then you define an equivalence relation [math] \sim [/math] on [math] V \times W [/math] such that

[math](v_1, w) + (v_2, w) \sim (v_1 + v_2, w) [/math]

[math](v, w_1) + (v, w_2) \sim (v , w_1 + w_2) [/math]

[math] c (v, w) \sim (c v, w) \sim (v , c w) [/math]

for [math]v, v_1, v_2 \in V, w, w_1, w_2 \in W, c \in \mathbb{K} [/math]

Now tensors are just the elements of [math] (V \times W) / \sim [/math].

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>>7784974

Actually you don't need vector spaces. You can do it with arbitrary modules over a ring.

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