TeXipedia

vdots

Represents vertical dots (ellipsis) in mathematical notation, commonly used to indicate pattern continuation in matrices or vertical sequences.

Overview

Essential for creating concise mathematical expressions by indicating vertical pattern continuation, particularly in matrices, determinants, and aligned equations.

  • Frequently used in linear algebra to show omitted middle rows of matrices
  • Helps maintain readability in tall mathematical structures
  • Often paired with \ddots or \cdots for showing patterns in multiple directions
  • Standard notation in academic papers and mathematical publications when displaying large mathematical structures

Examples

Vertical dots in a matrix to indicate omitted rows.

(a11a12a21a22⋮⋮an1an2)\begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \\ \vdots & \vdots \\ a_{n1} & a_{n2} \end{pmatrix} 
\begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \\ \vdots & \vdots \\ a_{n1} & a_{n2} \end{pmatrix}

Vertical dots between equations in a system.

x+y=1y+z=2⋮w+t=nx + y = 1 \\ y + z = 2 \\ \vdots \\ w + t = n 
x + y = 1 \\ y + z = 2 \\ \vdots \\ w + t = n

Vertical dots in a continued fraction representation.

a0+1a1+1a2+⋮a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \vdots}} 
a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \vdots}}