basis

introduction

%%visits: 5 A basis is the combination of span linear independence

We require that solving solutions to [[differential_equation]]s and similarly [[recurrence_relation]]s requires us to try a basis of possible solutions.

intuition

A basis is in a sense a coordinate system. Allows component wise things

We need the basis to be linearly independent so that there is only one way to represent a vector with our basis ## rigour e₁, e₂, e₃ are the standard basis $\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix},\begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix},\begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}$ ## exam clinic ## resources tags math__linear_algebra_1:__linear_algebra_2:__introduction_to_dynamical_systems:

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