Size & Dimension of a Matrix

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

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◇Overview

The size or dimension of a matrix is given by the number of rows (m) by the number of columns (n), written as $m \times n$. (Handout 1, Page 3)

◇Details / Theory

The size or dimension of a matrix is given by the number of rows (m) by the number of columns (n), written as $m \times n$. (Handout 1, Page 3) Example:
$A=\begin{bmatrix} 2 & 1 & 0 \\ -1 & 4 & 2 \\ 10 & 5 & 3 \\ 0 & 1 & 7 \end{bmatrix}$ has size $4 \times 3$. The (3,1) entry is $a_{31}=10$. (Handout 1, Page 4)

$B=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ has size $2 \times 2$. (Handout 1, Page 4)

$C=\begin{bmatrix} 1/2 & 3 & -2/3 \\ 4 & 1/3 & 5 \end{bmatrix}$ has size $2 \times 3$. (Handout 1, Page 4)

## Common Pitfalls Size is always rows × columns ($m \times n$), not columns × rows. A $3 \times 1$ matrix is NOT the same as a $1 \times 3$ matrix. ## Summary > TL;DR — The size of a matrix is $m \times n$ (rows × columns). Two matrices are the same size only if both $m$ and $n$ match. Size determines which operations are valid. ## Links **Related:** **Source / Reference:** ## References & Navigation - **Previous Topic:** [[Scalar Multiplication]] - **Next Topic:** [[Skew-Symmetric Matrix]] - **Related Notes:** [[Square Matrix]], [[Definition of a Matrix]], [[Matrices Detailed]]