# Vector Algebra

**Date:** June 17 2020

**Summary:** The algebraic functions one can execute on a vector

**Keywords:** ##zettel #vector ##mathematics #linearalgebra #algebra #multiplication #addition #scalar #archive

# Bibliography

Not Available

# Table of Contents

There are a few definitions of a vector. For this overview, I will use the definition that a vector is that which has the algebra of a vector space. The operations for vectors are straight-forward:

Vector Addition

$v + w = \begin{bmatrix} v_{1}\\ v_{2} \end{bmatrix} + \begin{bmatrix} w_{1}\\ w_{2} \end{bmatrix} = \begin{bmatrix} v_{1} + w_{1}\\ v_{2} + w_{2} \end{bmatrix}$
Scalar Multiplication

$2v = \left[
\begin{array}{c}
2v_{1} \\
2v_{2} \\
\end{array}
\right]$
Zelko, Jacob. *Vector Algebra*. https://jacobzelko.com/06172020134504-vector-algebra. June 17 2020.