TeXipedia

ddots

Represents a diagonal pattern of dots in matrices, indicating a continuation of elements along the diagonal.

Overview

Essential for displaying large or truncated matrices in mathematical notation, particularly when showing patterns or omitting repetitive elements.

  • Commonly used in linear algebra to show matrix structure without writing all elements
  • Pairs naturally with \vdots and \cdots for comprehensive matrix notation
  • Particularly useful when representing block matrices or demonstrating matrix patterns
  • Often appears in academic papers and textbooks where space conservation is important

Examples

Diagonal dots in a matrix showing a pattern continuation.

(a11a12⋯a1na21a22⋯a2n⋮⋮⋱⋮am1am2⋯amn)\begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{pmatrix} 
\begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{pmatrix}

Abbreviated display of a block diagonal matrix.

(A000⋱000B)\begin{pmatrix} A & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & B \end{pmatrix} 
\begin{pmatrix} A & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & B \end{pmatrix}

System of recursive equations with pattern continuation.

x1=a1x2=a2⋱xn=an\begin{array}{rcl} x_1 &=& a_1 \\ x_2 &=& a_2 \\ &\ddots& \\ x_n &=& a_n \end{array} 
\begin{array}{rcl} x_1 &=& a_1 \\ x_2 &=& a_2 \\ &\ddots& \\ x_n &=& a_n \end{array}