3.2 The ith Coefficient of a Column Vector

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 3.1 Column Vector

Properties: N/A
Sufficiencies: N/A
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The

i

th Coefficient of a Column Vector

Let $\vec{x} \in R^{n \times 1}$ be a column vector, given by

\vec{x} = [\begin{matrix} x_{1} \\ x_{2} \\ ⋮ \\ x_{n} \end{matrix}]

The real number $x_{i} \in R$ in the $i$ th row of $\vec{x}$ is called the $i$ th coefficient of vector $\vec{x}$ for $i \in {1, 2, \dots, n}$ . We refer to the $i$ th coefficient of $\vec{x}$ using the following notation:

Subscript notation: $x_{i}$
Entry operator notation: entry $_{i} (\vec{x})$ returns the $i$ th entry of $\vec{x} \in R^{n}$ .
Matrix index notation: $x (i, 1)$ refers to the entry in the $i$ th row and 1st column.

Remark. We will mainly use subscript notation and the matrix index notation.

Subscript notation is compact & straightforward.
Matrix index notation is used to code in MATLAB.
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