Math/Linear algebra
Linear independence
데먕
2019. 10. 10. 14:42
1. Overview
2. Description
2.1 Definition
A set of M vectors is independent if each vector points in a geometric dimension not reachable using other vectors in the set.
Any set of M>N vectors in $\mathbb{R}^{N}$ is dependent
Any set of $M\leq N$ vectors in $\mathbb{R}^{N}$ could be independent
2.2 How to determine whether a set is independent
Step 1: Count vectors and compare with $R^{N}$
Step 2: Check for 0's in corresponding (or all) elements
Step 3: Educated guess and test
Step 4: Matrix rank method
3. Example
3.1 Dependent set
3.2 Independent set
