3.5 Equal Column Vectors

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

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

Equal Column Vectors

Let $\vec{x} \in R^{n}$ and $\vec{y} \in R^{m}$ be column vectors. These vectors are equal iff:

$n = m$ , vectors have same number of rows
$x_{i} = y_{i}$ for all $i \in {1, 2, \dots, n}$ .

In other words, when we look at the vector equality $\vec{x} = \vec{y}$ , the equality is only true if the dimensions and individual coefficients are identical.

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