Definition of a Matrix

Tags: #◇CSMATH2 #◇Linear Algebra #◇Computational Mathematics #◇Matrices #◇Matrix Operations #◇Computer Science #◇Vector Spaces #◇Linear Transformations

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◇Overview

A matrix A is a rectangular array of real numbers, formally written as:

◇Details / Theory

A matrix A is a rectangular array of real numbers, formally written as:
$A=\begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix}=[a_{ij}]$
(Handout 1, Page 3) The numbers $a_{ij}$ are called entries or elements of A. $a_{ij}$ refers to the (i, j) entry, located at the i-th row and j-th column. (Handout 1, Page 3)
PN: Remember the convention: row index first ($i$), column index second ($j$). This is crucial for indexing and operations.

◇Common Pitfalls

Confusing row index and column index — always row first ($i$), column second ($j$). Referring to $a_{ij}$ as "column $i$, row $j$" — it's the opposite.

◇Summary

TL;DR — A matrix is a rectangular array of real numbers. Entry $a_{ij}$ is at row $i$, column $j$. Convention: row index always comes first.

◇Links

Related: Source / Reference:

◇References & Navigation

• Previous Topic: ◇Column Matrix
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• Related Notes: ◇Elementary Matrices, ◇Properties of Matrix Operations, ◇Matrices Detailed