Editing Linear algebra (section)

=== Study of complex systems ===
{{see also|Complex system}}
Most physical phenomena are modeled by [[partial differential equation]]s. To solve them, one usually decomposes the space in which the solutions are searched into small, mutually interacting [[Discretization|cells]]. For [[linear system]]s this interaction involves [[linear function]]s. For [[nonlinear systems]], this interaction is often approximated by linear functions.{{efn|This may have the consequence that some physically interesting solutions are omitted.}}This is called a linear model or first-order approximation. Linear models are frequently used for complex nonlinear real-world systems because they make [[Parametrization (geometry)|parametrization]] more manageable.<ref>{{Cite book |last=Savov |first=Ivan |title=No Bullshit Guide to Linear Algebra |publisher=MinireferenceCo. |year=2017 |isbn=9780992001025 |pages=150–155 |language=en}}</ref> In both cases, very large matrices are generally involved. [[Weather forecasting]] (or more specifically, [[Parametrization (atmospheric modeling)|parametrization for atmospheric modeling]]) is a typical example of a real-world application, where the whole Earth [[atmosphere]] is divided into cells of, say, 100&nbsp;km of width and 100&nbsp;km of height.