Vectors in Rn Pt1

the rescource page can be found here notes

lets start of with the most basic quantifiable aspect of linear algebra. The humble vector. so what is a vector???
to explain that lets begin with what a vector is not. a vector is not a certain game on android that gets you to run for hours. a vector is a quantity. Now there are more types of quantities than just the vector. If you were to count the number of steps you have walked today on your fit-bit, or the temperature of the weather in your area to know what you should wear today. those measurements are not vectors but scalers, and its actually a very smart name for them that we will come back to in a moment. if you were to take that measurement such as the number of steps you've taken and add another piece of information, your direction, you will have recorded a vector. and there you go by definition a vector is a quantity that posses both magnitude and direction. we usually express these things by arrows. you may see the notes for an example of how they look. Because we love computer science here as well lets code this quantity.

I've written this in Java and posted it on my resource page that can be found here. I have sectored the source code off so that as you complete sections in this text you may reference my code and build up your own.

lets move onto section 2 now vector operations. if you are following along in the code we will move onto the operations package, the vectors class. lets begin with vector addition. if you have say two vectors in R2 [0, 1] [1, 1]

if we want to add these we will take each individual component and add them
[0+1, 1+1] = [1, 2].

remember above here when we were talking about those simpler quantities called scalers here I will explain them in a little more detail. you simply take the scaler a and multiply each component of the vector S e.g.:
a[1,2,3,4] =
[1a,2a,3a,4a] =
[a,2a,3a,4a]

you see what i mean by its such a clever name the scaler simply scales the vector to a greater magnitude but it will always still point in the same direction as before it was put through scaler multiplication.

thanks for reading here is a vector potato