A Toeplitz matrix is one in which each descending diagonal from left to right is constant. Given that structure, matrix operations are sometimes much faster. Where are Toeplitz matrices likely to occur?

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    $\begingroup$ Some applications are boundary value problems, convolutions, and simulations of "small-world" networks. $\endgroup$ – Fabio Somenzi Oct 7 '18 at 23:32
  • $\begingroup$ I was hoping for a specific example. A "small-world" network of what exactly? $\endgroup$ – Brian Spiering Oct 8 '18 at 4:00
  • $\begingroup$ See this for a discussion of small-world networks. A way to construct the adjacency matrices of such graphs is to start with a Toeplitz matrix, which guarantee connectivity, and add random "shortcut" edges that reduce distances. $\endgroup$ – Fabio Somenzi Oct 8 '18 at 5:17

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