$$

Reading materials

1. Is this vector in the span? Case of yes
2. Is this vector in the span? Case of no
3. Is this vector in the affine subspace? Case of yes
4. Is this vector in the affine subspace? Case of no
5. Video: affine subspace
6. How to solve a system of linear equations?
7. Video: parametrize a system
8. Video: find particular and homogeneous solution
9. How to compare two sets?
10. How to compare two spans?
11. Midterm 1: Questions to ponder
12. SMART goals
13. Vector space: Hefferon Two.I.1
14. Subspace: Hefferon Two.I.2
15. Kahoot! –- Vector space
16. Linear independence: Hefferon Two.II
17. Is this set linear independent? Case of yes
18. Is this set linear independent? Case of no
19. Linear independent or not?
20. How to find a basis of the kernel?
21. How to find a basis of the row space?
22. How to find a basis of the column space?
23. Midterm 2: Questions to ponder
24. Vector representation: Hefferon Two.III.1
25. Function: Hefferon Appendix or 1121 la function basics
26. Properties of a function
27. Isomorphism: Hefferon Three.I
28. Is this function injective?
29. Is this function surjective?
30. Homomorphism (linear function): Hefferon Three.II
31. Matrix representation in
    ${\mathbb{R}}^n$
32. Matrix representation: Hefferon Three.III
33. Matrix is a price table
34. Matrix representation in a vector space
35. Change of basis Hefferon Three.V
36. Kernel and range of a linear function
37. Final: Questions to ponder

The following terminologies are interchangeable:

1. homomorphism, linear function, linear map
2. null space, kernel
3. vector representation of the vector
   $\mathbf{x}$ with resepect to the basis
   $\beta$:
   $[\mathbf{x}{]}_{\beta }$,
   ${\mathrm{Repr}}_{\beta }(\mathbf{x})$
4. matrix representation of the function
   $f$ with respect to the bases
   $\alpha$ and
   $\beta$:
   $[f{]}_{\alpha }^{\beta }$,
   ${\mathrm{Repr}}_{\alpha ,\beta }(f)$

Recomended reading schedule

Reading the textbook is the best way to get a comprehensive understanding of a subject. Here we assign some sections of the textbook for reading. Aside from them, there are some videos from 3Blue1Brown with great illustrations of the related concept.

Linear geometry

Week of 9/4

• Gilbert Strang: Linear Algebra vs Calculus
• Chapter 0: Essence of linear algebra preview
• Hefferon –- One.I.1

Week of 9/11

• Chapter 1: Vectors, what even are they?
• Hefferon –- One.I.2 ~ 3

Week of 9/18

• Chapter 2: Linear combinations, span, and basis vectors
• Hefferon –- One.II.1

Week of 9/25

• Chapter 3: Linear transformations and matrices
• Hefferon –- One.II.2 ~ III.2

Week of 10/2

• Chapter 4: Matrix multiplication as composition
• Hefferon –- Topic: Computer Algebra Systems

Week of 10/9

• Chapter 5: Three-dimensional linear transformations
• Hefferon –- Topic: Accuracy of Computations

Linear spaces

Week of 10/16

• Chapter 6: The determinant
• Hefferon –- Two.I.1 ~ 2

Week of 10/23

• Chapter 7: Inverse matrices, column space and null space
• Hefferon –- Two.II.1

Week of 10/30

• Chapter 8: Nonsquare matrices as transformations between dimensions
• Hefferon –- Two.III.1 ~ 2

Week of 11/6

• Chapter 9: Dot products and duality
• Hefferon –- Two.III.3 ~ 4

Week of 11/13

• Chapter 10: Cross products
• Hefferon –- Topic: Fields

Linear functions

Week of 11/20

• Chapter 11: Cross products in the light of linear transformations
• Hefferon –- Three.I.1 ~ II.1

Week of 11/27

• Chapter 12: Cramer's rule, explained geometrically
• Hefferon –- Three.II.2 ~ III.1

Week of 12/4

• Chapter 13: Change of basis
• Hefferon –- Three.III.2 ~ IV.3

Week of 12/11

• Chapter 16: Abstract vector spaces
• Hefferon –- Three.IV.4 ~ V.2

More…

• Chapter 14: Eigenvectors and eigenvalues
• Chapter 15: A quick trick for computing eigenvalues
• Hefferon –- Three.VI.1 ~ 3
• Hefferon –- Topic: Line of Best Fit

References

• Texkbook: Linear Algebra by Jim Hefferon
• Texkbook: Linear Algebra Done Right by Sheldon Axler
• YouTube playlist: Essence of linear algebra by 3Blue1Brown
• YouTube playlist: Linear Algebra by The Math Sorcerer
• Online resource: 3Blue1Brown
• Online resource: LA Tea website
• Online resource: Intuitive Math
• Online resource: Khan Academy Linear Algebra

Linear Algebra from 3Blue1Brown

• Chapter 0: Essence of linear algebra preview
• Chapter 1: Vectors, what even are they?
• Chapter 2: Linear combinations, span, and basis vectors
• Chapter 3: Linear transformations and matrices
• Chapter 4: Matrix multiplication as composition
• Chapter 5: Three-dimensional linear transformations
• Chapter 6: The determinant
• Chapter 7: Inverse matrices, column space and null space
• Chapter 8: Nonsquare matrices as transformations between dimensions
• Chapter 9: Dot products and duality
• Chapter 10: Cross products
• Chapter 11: Cross products in the light of linear transformations
• Chapter 12: Cramer's rule, explained geometrically
• Chapter 13: Change of basis
• Chapter 14: Eigenvectors and eigenvalues
• Chapter 15: A quick trick for computing eigenvalues
• Chapter 16: Abstract vector spaces