What are Tensor Diagrams?
+Tensor diagrams are a powerful visual tool for representing and manipulating tensors, which are generalizations of vectors and matrices to higher dimensions. They provide an intuitive way to understand complex tensor operations and identities.
+ +For example, consider the matrix multiplication of A and B:
+ ++ A B + | \ / | + | X | + | / \ | + Y ++
This diagram represents (AB)_ik = sum_j A_ij B_jk. The crossing lines indicate the summation over the index j.
+ +Tensor diagrams are particularly useful because they:
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- Simplify complex tensor expressions +
- Make it easy to spot patterns and symmetries +
- Help in deriving new identities +
- Provide a universal language for tensor operations across different fields +
About the Book
The Tensor Cookbook is a comprehensive guide to tensors, using the visual language of tensor diagrams. It closely follows the legendary "Matrix Cookbook" while providing a new way to understand and appreciate tensor operations through diagrams.