# Questions tagged [tensor-rank]

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### What does doing a tensor network contraction "for bond dimension k" mean?

I’m a tensor-network newbie and am working through Bridgeman and Chubb’s “Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks” (arXiv:1603.03039v4). At the end of Chapter 1, ...
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### Has there been any research on faster tensor inner products?

Matrix multiplication is a well studied problem which is recently back in the news due to deepmind. That got me wondering has anyone looked at the more general problem of faster tensor multiplication? ...
208 views

### Computing dual of the spectral norm of tensor of order 3

It is shown in http://www.stat.uchicago.edu/~lekheng/work/jacm.pdf that computing the spectral norm (see Definition 6.6) of a $3^{rd}$ order tensor $T \in \mathbb{R}^{d_1 \times d_2 \times d_3}$ is NP-...
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### Deciding bound on Tensor Rank for a fixed value

This question is related to a previous unanswered question of mine. Please see that question for background. When Håstad proved that computing tensor rank is NP-complete, the rank in question was ...
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263 views

### normalized tensor rank

Is there such a thing as a "normalized tensor rank" for non-square tensors (i.e. a tensor with different sizes along each mode)? For example: If a 3rd order tensor (dimensions = 60 x 120 x 30) has ...
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928 views

### Complexity of Tensor Rank over an Infinite Field

A tensor is a generalization of vectors and matrices to higher dimensions and the rank of a tensor also generalizes the rank of a matrix. Namely, the rank of a tensor $T$ is the minimum number of rank ...
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178 views

### What are contravariant tensors of type m choose 0

I am not sure if the following question falls within the scope of this site; if it does not, I will request the moderators to take appropriate action I have been going through Jin-Yi Cai's expository ...
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