Linear algebra Vectors and stuff
YLinear algebra is used for tons of stuffs
Search rankings, big data and Ai. It is one of the most aplied areas of maths and in my oppinion one the more interesting ones.
We got a warning the it’s a lot mote abstract in comparison to other maths subjects like calculus. Every thing is in the definition and there is not much calculations needed to be done.
Vectors
There are three ways of looking at vectors
Like a physisist
Like a computer scientist
Like a mathmatician
Like a physisist
In physics it is a vlaue with a length and a direction, look at forces, speed, acceleration
For example you accellerate at a certian rate in a certain direction, in this way you can also use vectors to describe a position in a cordinate system.
Like a computer scientist
Here it is seen as a list of numbers, if you have ever touched c++ think std::vector
Like a mathmatician
Whatever fulfills the axiom.
The axiom has 11 parts
You can add two vectors and they end up in thsame dimensional space
You can add them in any order
The same if you have more than two
If you ad a vector X with the zero vector you will get X
if you add the a vector and the negative version of it you’ll get
You can multiply a vector with a scalar and get a new vector
you can do the previous one in any order
and it spreds into a parenthesis they way you expect
both ways
And if you multiply it with one you end up with, you guesed it the same vector you started with
Addition is quite simple
Subtraction also but not the expected result really
They are paralell if you can get one vector by multiplying another by a scalar
We can have vectors in imaginary dimensions
Length is apperently called norm who knew but that comes from vector.length()
If the norm is 1 the you have a unit vector is nize to use at times you now
You could create a linear kombination
Scalar product in swedish dot product in global speaks
two and three dimensions you can think geometry but in n dimensions that’s a bit hard but apperently you can do it kinda
And it works as you might expect
This was a first thing usefull for me and only me I cleared my first exam i’m happy