2025-04-03

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 \(f_n(x) \in C^0(\mathbb{R})\).


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