Tensor network: <a href="https://en.wikipedia.org/wiki/Tensor_network" rel="nofollow">https://en.wikipedia.org/wiki/Tensor_network</a> :<p>> <i>The wave function is encoded as a tensor contraction of a network of individual tensors.[3] The structure of the individual tensors can impose global symmetries on the wave function (such as antisymmetry under exchange of fermions) or restrict the wave function to specific quantum numbers, like total charge, angular momentum, or spin. It is also possible to derive strict bounds on quantities like entanglement and correlation length using the mathematical structure of the tensor network.[4] This has made tensor networks useful in theoretical studies of quantum information in many-body systems. They have also proved useful in variational studies of ground states, excited states, and dynamics of strongly correlated many-body systems. [5]</i><p>...<p>Tensor product network: <a href="https://en.wikipedia.org/wiki/Tensor_product_network" rel="nofollow">https://en.wikipedia.org/wiki/Tensor_product_network</a><p>Tensor product model transformation of : <a href="https://en.wikipedia.org/wiki/Tensor_product_model_transformation" rel="nofollow">https://en.wikipedia.org/wiki/Tensor_product_model_transform...</a><p>HOSVD; Higher-Order Singular Value Decomposition<p>TP model transformation in control theory: <a href="https://en.wikipedia.org/wiki/TP_model_transformation_in_control_theory" rel="nofollow">https://en.wikipedia.org/wiki/TP_model_transformation_in_con...</a><p>...<p><a href="https://tensornetwork.org/diagrams/" rel="nofollow">https://tensornetwork.org/diagrams/</a> :<p>> <i>Let us look at some example diagrams for familiar low-order tensors:</i><p>Tensor diagram = Penrose graphical notation > Tensor operations:
<a href="https://en.wikipedia.org/wiki/Penrose_graphical_notation" rel="nofollow">https://en.wikipedia.org/wiki/Penrose_graphical_notation</a> ... Trace Diagrams, Spin Network, [... Knots and Quantum Invariant theories, Chern-Simons Theory, Topology]
I don't get it, what's cool about it? Einstein notation seems good enough for most of the things and they are equivalent. Is there anything interesting (i.e. new) that this notation allow?