the cedar ledge

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

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Table of Contents

  1. How To Cite
  2. References
  3. Discussion:

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:

  1. Vector Addition

v+w=[v1v2]+[w1w2]=[v1+w1v2+w2] 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}

  1. Scalar Multiplication

2v=[2v12v2] 2v = \left[ \begin{array}{c} 2v_{1} \\ 2v_{2} \\ \end{array} \right]

How To Cite

Zelko, Jacob. Vector Algebra. https://jacobzelko.com/06172020134504-vector-algebra. June 17 2020.

References

Discussion:

CC BY-SA 4.0 Jacob Zelko. Last modified: November 24, 2023. Website built with Franklin.jl and the Julia programming language.