Aidyn Crosby

2022-10-02

Strange math notation, vertical bar with parentheses.

So I was reading "Resistance Distance" (D. J. Klein, M. Randić) (Journal of Mathematical Chemistry 12(1993)81-95) when I came up with strange notation.

From the paper:

The graph adjacency matrix is defined as:

${A}_{xy}=(x|A|y)=\{\begin{array}{ll}1/{r}_{xy}& x\sim y\\ 0& \text{otherwise}\end{array}$

The graph degree matrix of a graph is defined as:

${\mathrm{\Delta}}_{xy}=(x|\mathrm{\Delta}|y)=\delta (x,y)\sum _{z}^{\sim x}1/{r}_{xy}$

$|\varphi )\equiv \sum _{x}|x)$

My main question is what does the combination of the vertical bar parentheses mean. Thanks in advance.

So I was reading "Resistance Distance" (D. J. Klein, M. Randić) (Journal of Mathematical Chemistry 12(1993)81-95) when I came up with strange notation.

From the paper:

The graph adjacency matrix is defined as:

${A}_{xy}=(x|A|y)=\{\begin{array}{ll}1/{r}_{xy}& x\sim y\\ 0& \text{otherwise}\end{array}$

The graph degree matrix of a graph is defined as:

${\mathrm{\Delta}}_{xy}=(x|\mathrm{\Delta}|y)=\delta (x,y)\sum _{z}^{\sim x}1/{r}_{xy}$

$|\varphi )\equiv \sum _{x}|x)$

My main question is what does the combination of the vertical bar parentheses mean. Thanks in advance.

Johnny Parrish

Beginner2022-10-03Added 12 answers

Here is a community wiki answer so the question can be closed.

This is bra-ket notation, as commonly used in physics.

This is bra-ket notation, as commonly used in physics.

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