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I'm trying (and failing miserably) to understand tensors, and I have a quick question: is the inner product of a rank n tensor with another rank n tensor always a scalar? And also is the inner product of a rank n tensor with a rank n-1 tensor always a rank n-1 tensor that has been transformed/stretched in some way?

I would also be really grateful if anyone has a simple explanation of rank 2 tensors. I've looked up several posts on PF and elsewhere but I still don't really get them...

Thank you!

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# Is the inner product of two rank n tensors a scalar?

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