Data Matrix

Definition

The data matrix corresponding to a data set of $n$ records which are length $d$ tuples of real numbers is the $n$ by $d$ matrix whose $i$th row is the $i$ element of the data set. Some authors refer to the data matrix as the design matrix.

Notation

Let $(a^1, \dots , a^n)$ where $a^i \in \R ^n$ for $i = 1, \dots , n$. Let $A$ be the $n \times d$ matrix whose rows are the $a^i$. Then $A$ is the data matrix of $(a^1, \dots , a^n)$. In other words,

\[ A = \bmat{ (a^1)^\top \\ \cdots \\ (a^n)^{\top }}. \]