Matrices as Tensor Network Diagrams

Like a matrix, an $n$-tensor can be  represented by a node with one edge for each dimension. A quick check: A matrix was described as a single node with one edge for each vector space, yet the picture above has two nodes. A similar picture holds for matrix-vector multiplication: a matrix $M$ multiplied by a vector $\mathbf{v}$ results in another vector $M\mathbf{v}$, which is a node with one free edge.

Source: www.math3ma.com