For questions related to Penrose graphical notation (or tensor diagram notation). It is a (usually handwritten) visual depiction of multilinear functions or tensors. A diagram in the notation consists of several shapes linked together by lines.
Multilinear algebra
Each shape represents a multilinear function. The lines attached to shapes represent the inputs or outputs of a function, and attaching shapes together in some way is essentially the composition of functions.Tensors
A particular tensor is associated with a particular shape with many lines projecting upwards and downwards, corresponding to abstract upper and lower indices of tensors respectively. Connecting lines between two shapes corresponds to contraction of indices. One advantage of this notation is that one does not have to invent new letters for new indices. This notation is also explicitly basis-independent.Matrices
Each shape represents a matrix, and tensor multiplication is done horizontally, and matrix multiplication is done vertically.
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