# Eigenvectors with distinct eigenvalues are linearly independent.

math.la.t.mat.eigvec.linindep

# Geometry of eigenvectors

Definition of the eigenspace corresponding to an eigenvector $\lambda$ (and proof that this is a vector space); analysis of simple matrices in R^2 and R^3 to visualize the "geometry" of eigenspaces; proof that eigenvectors corresponding to distinct eigenvectors are linearly independent

##### math.la.d.mat.eigsp
Created On
August 25th, 2017
5 years ago
Views
2
Type
Video
Language
English
Content Type
text/html; charset=utf-8

# Properties of Eigenvalues and Eigenvectors - A First Course in Linear Algebra

The previous section introduced eigenvalues and eigenvectors, and concentrated on their existence and determination. This section will be more about theorems, and the various properties eigenvalues and eigenvectors enjoy. Like a good 4×100 meter relay, we will lead-off with one of our better theorems and save the very best for the anchor leg.