Vectors are a collection of co-ordinates that a point has in a given space. They are defined by their magnitude and direction.

For n-dimensions there are n-coordinates in the given space.

Unit vector has a magnitude of one. To find the unit vector of any vector divide each element of the vector by the vectors length.

The projection of vector x on vector y can be found by dividing the dot product of x and y by the magnitude of the vector y and multiplied by vector y . The projection of vector x is in the direction of y vector.

This is an example on projecting vector x on vector y.

Above is an example to calculate the angle between two vectors.

Two vectors are said to be orthogonal when the angle between them is 90°. That is the dot product between the vectors should be zero.

Matrices :

Matrices are a collection of row vectors or column vectors. Data we deal are mostly is in the form of matrices. We manipulate these matrices to find relations and make predictions.

Here is a useful playlist :

https://www.youtube.com/playlist?list=PL2jykFOD1AWazz20_QRfESiJ2rthDF9-Z