For a Machine Learning view of Linear Algebra you can go through chapter 2 of the Deep Learning Book available online
'Deep Learning, Chapter 2: Linear Algebra':http://www.deeplearningbook.org/contents/linear_algebra.html

If you want to get a bit deeper, Gilbert Strang has great Linear Algebra course taught MIT is on youtube. He explains things very clearly and with a lot of simple example. I highly recommend his course as well.

I recently attended a Q&A session in San Francisco about the linear algebra chapter with Yaroslav Bulatov (Open Ai, previously Google Street View).
'Yaroslav Bulatov (OpenAi) Q&A Deep Learning Book, Chapter 2: Linear Algebra':https://www.youtube.com/watch?v=NMhK2A_N0Nc
 
If you want get a better base of knowledge, Gilbert Strang's Linear Algebra course taught MIT is on youtube. He explains things very clearly and with a lot of simple examples. I highly recommend his course as well.

'Gilbert Strang MIT Linear Algebra Video Lectures':https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/
You may want to play it at 1.5 or 2x speed though :).

If you just want some visual intuition behind eigen values and eigen vectors there's a very good blog post:
'Eigen Vectors and Eigen Values explained visually':http://setosa.io/ev/eigenvectors-and-eigenvalues/
where the authors have some dynamic visualizations so you can move things around and observe the effects.
 

There are lots of applications of linear algebra:
- Pagerank, the algorithm behind Google's success is based on eigen values and eigen vectors
- The winning entry in the Netflix Prize was based on Singular Value Decomposition
- 3D games use matrix multiplications for computing rotations, translations, shearing transforms
- in machine learning figuring out if your data is well conditioned for Stochastic Gradient Descent corresponds to having a small ratio between the min and max eigen value of the hessian matrix

- and of course they are sometime used in coding contest competitions :)

- and of course they are sometime used in coding contest competitions :)
 
Have fun!