How do you translate back and forth between coordinate systems that use different basis vectors?

Watch the full "Essence of linear algebra" playlist here: www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

1. Essence of linear algebra preview
2. Vectors, what even are they?
3. Linear combinations, span, and basis vectors
4. Linear transformations and matrices
5. Matrix multiplication as composition
6. Three-dimensional linear transformations
7. The determinant
8. Inverse matrices, column space and null space
9. Nonsquare matrices as transformations between dimensions
10. Dot products and duality
11. Cross products
12. Cross products in the light of linear transformations
13. Change of basis
14. Eigenvectors and eigenvalues
15. Abstract vector spaces

This introduces the "Essence of Linear Algebra" series, aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course.

This course is perfect for any high school student interested in exploring the world of Linear Algebra, which any math and engineering student will face in their college years. Furthermore, this course is perfect for any university and adult learner who wants an intuitive, original, and entertaining explanation of simple and complex Linear Algebra concepts.