Monthly Archives: October 2015

A Story of Basis and Kernel – Part I: Function Basis

Author: Changyue Song

1. Review of Basis Concept

We know that everything in the world can be decomposed into the combination of the basic elements. For example, water is the combination of hydrogen and oxygen. Similarly, in mathematics, basis is used to represent various things in a simple and unified way.

In \( \mathcal{R}^n \) space, we can use \( n \) independent vectors to represent any vector by linear combination. The \( n \) independent vectors can be viewed as a set of basis. There are infinite basis sets in \( \mathcal{R}^n \) space. Among them, basis vectors that are orthogonal to each other are of special interests.… Read more