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linear_algebra.md

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 # Linear Algebra
 
-In [mathematics](math.md) linear algebra is an extension of the classical elemental algebra ("operations with numbers/variables") to [vectors](vector.md) and [matrices](matrix.md) ("arrays of numbers"). It is a basic tool of advanced mathematics and [computer science](computer_science.md) (and many other sciences) and at least at the very basic level should be known by every [programmer](programmer.md).
+In [mathematics](math.md) linear algebra is an extension of the classical elemental algebra (which means the basic "operations with numbers/variables") to [vectors](vector.md) and [matrices](matrix.md) (kind of "operations with arrays of numbers"). It is a basic tool of advanced mathematics and [computer science](computer_science.md) (and many other sciences) and at least at the very basic level should be known by every [programmer](programmer.md).
 
-Why is it called *linear* algebra? Basically because it deals with [linear equations](linear.md) which is kind of about proportionality, function plots being lines etc. A mathematician will probably puke at this explanation but it gives some intuition :)
+Why is it called *linear* algebra? Basically because it deals with [linear equations](linear.md) which is kind of about proportionality, function plots being lines etc. A mathematician will probably puke at this explanation but it gives some intuition :) See also [linearity](linearity.md).
 
 ## Basics
 
 In "normal" algebra our basic elements are [numbers](number.md); we learn to add then, multiply then, solve equation with them etc. In linear algebra we call these "single numbers" **[scalars](scalar.md)** (e.g. 1, -10.5 or [pi](pi.md) are scalars), and we also add more complex elements: **[vectors](vector.md)** and **[matrices](matrix.md)**, with which we may perform similar operations, even though they sometimes behave a bit differently (e.g. the order in multiplication of matrices matters, unlike with scalars).
 
-Vectors are basically sequences ([arrays](array.md)) of numbers, e.g. a vector of length 3 may be [1.5, 0, -302]. A matrix can be seen as a [two dimensional](2d.md) vector (a 2D array of numbers), e.g. a 2x3 matrix may look like this:
+Vectors are, put in a very simplified and slightly incorrect way, sequences ([arrays](array.md)) of numbers, e.g. a vector of length 3 may be [1.5, 0, -302]. A matrix can similarly be seen as a [two dimensional](2d.md) "array of numbers", e.g. a 2x3 matrix may look like this:
 
 ```
 |1  2.5 -10|
 |24 -3   0 |
 ```
 
-Similarly we may see vectors as matrices that have either only one column, so called **column vectors**, or only one row, so called **row vectors** -- it is only a matter of convention which type of vectors we choose to use (this affects e.g. "from which side" we will multiply vectors by matrices). For example a column vector
+We may kind of see vectors as matrices that have either only one column, so called **column vectors**, or only one row, so called **row vectors** -- it is only a matter of convention which type of vectors we choose to use (this affects e.g. "from which side" we will multiply vectors by matrices). I.e. we choose which kind of vectors we'll use and then keep using only that kind. For example a row vector
 
 ```
 |5 7.3 -2|
 ```
 
-is really a 3x1 matrix that as a row vector (1x3 matrix) would look as
+is really a 3x1 matrix that as a column vector (1x3 matrix) would look as
 
 ```
 |5  |