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Miloslav Ciz 2022-08-01 17:33:00 +02:00
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linear_algebra.md
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@ -17,4 +17,8 @@ Vectors are basically sequences ([arrays](array.md)) of numbers, e.g. a vector o
Why work with vectors and matrices? Because these can represent certain things we encounter in math and programming better than numbers, e.g. vectors may represent points in space or velocities with directions and matrices may represent transformations.
With vectors and matrices we can perform similar operations as with "normal numbers", i.e. addition, subtraction, multiplication, but there are also new operations and some operations may behave differently. E.g. when dealing with vectors, there are multiple ways to "multiply" them: we may multiply a vector with a scalar but also a vector with vector (and there are multiple way to do this such as [dot product](dot_product.md) and [cross product](cross_product.md)). Matrix multiplication is, unlike multiplication of real numbers, non-[commutative](commutativity.md) (A times B doesn't necessarily equal B times A), but its still [distributive](distributivity.md). We can also multiply vectors with matrices but only those that have "compatible sizes". And we can also solve equations and systems of equations which have vectors and matrices in them.
With vectors and matrices we can perform similar operations as with "normal numbers", i.e. addition, subtraction, multiplication, but there are also new operations and some operations may behave differently. E.g. when dealing with vectors, there are multiple ways to "multiply" them: we may multiply a vector with a scalar but also a vector with vector (and there are multiple way to do this such as [dot product](dot_product.md) and [cross product](cross_product.md)). Matrix multiplication is, unlike multiplication of real numbers, non-[commutative](commutativity.md) (A times B doesn't necessarily equal B times A), but its still [distributive](distributivity.md). We can also multiply vectors with matrices but only those that have "compatible sizes". And we can also solve equations and systems of equations which have vectors and matrices in them.
## See Also
- [analytic geometry](analytic_geometry.md)