Linear algebra formalism: Difference between revisions
Created page with "Aspects of tuning theory are often described in the language of '''linear algebra.''' {{Todo|complete intro|inline=1}} == Monzos and vectors == {{Todo|complete section|inline=1}} == Vals and covectors == {{Todo|complete section|inline=1}} == Mappings and matrices == {{Todo|complete section|inline=1}} == Matrix operations == {{Todo|complete section|inline=1}} === Dot product === The dot product is a way to combine two vectors to get out a single number. Say we want..." |
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== Monzos and vectors == | == Monzos and vectors == | ||
{{Todo|complete section|inline=1}} | {{Todo|complete section|inline=1}}A vector is a list of numbers, written like so: <math> \begin{pmatrix} | ||
-2\\ | |||
0\\ | |||
1 | |||
\end{pmatrix} </math>. | |||
== Vals and covectors == | == Vals and covectors == | ||
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== Mappings and matrices == | == Mappings and matrices == | ||
{{Todo|complete section|inline=1}} | {{Todo|complete section|inline=1}}A matrix is a grid of numbers, written like so: | ||
<math> | |||
\begin{bmatrix} | |||
1 & 0 & -4\\ | |||
0 & 1 & 4 | |||
\end{bmatrix} | |||
</math> | |||
This matrix can be thought of as a "function" that you apply to a vector to get out another vector. This matrix has 3 columns, meaning the vector it takes as an "input" will have 3 elements, and it has 2 rows, meaning the vector you get out will have 2 elements. So, this is a "function" down from 3-dimensional space to 2-dimensional space. | |||
== Matrix operations == | == Matrix operations == | ||