Linear Algebra
Table of Contents
1. Facts
- Real symmetric matrix => n orthonormal eigenvectors
2. Example of linearly independent functions in C0
Let \(n \in N\)
\begin{align} f_n(x) = \begin{cases} 0 &\textrm{ for } x \in (-\infty, 1/n] \\ x - 1/n &\textrm{ for } x > 1/n \\ \end{cases} \end{align}This sequence of function is linearly independent and \(f_n(x) \in C^0(\mathbb{R})\).