8.11 Colon Notation

Types: 8.12 Column Operator, 8.13 Column Partition of a Matrix
Examples: N/A
Constructions: N/A
Generalizations: N/A

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Colon Notation

A useful way to refer to individual columns/rows of a matrix is to use colon notation.

If $A \in R^{m \times n}$ , then $A (:, k) \in R^{m \times 1}$ stands for the $k$ th column of $A$

A (:, k) = [\begin{matrix} a_{1 k} \\ a_{2 k} \\ ⋮ \\ a_{m k} \end{matrix}]

for $k \in {1, 2, \dots, n}$ .

A (i, :) = [\begin{matrix} a_{i 1} & a_{i 2} & \dots & a_{i n} \end{matrix}]

for $i \in {1, 2, \dots, m}$ .

Remark. This notation originated from MATLAB. This notation will be extremely useful when working with vectors.
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