I'm not really sure this question is proper for MathExchange but I have found it more suitable than StackOverFlow.
So, I'm taking the course of Data Structures and Algorithms and we got some example for a hashing function family described by a matrix.
I also found it be taught by MIT through this lesson: https://www.youtube.com/watch?v=z0lJ2k0sl1g&t=3424s
And I have some questions regarding this example as shown during 32:00 to 36:30:
I begun losing him in 33:24 when he suggests to represent every key by the base of $m$ and this key is somehow translated to a vector of $m$ coordinates, and the process of transforming it to a vector is not really understandable.
Then he takes some key, representing it by a column vector, defining a dot product which generates hashes to other keys (?).
So, these two points are pretty not clear for me, and I also tried to think of a suitable matrix for this kind of hash function couldn't find one.
Can someone clarify these issues?