{%hackmd 5xqeIJ7VRCGBfLtfMi0_IQ %}

## Reading materials

1. [Is this vector in the span? Case of yes](https://hackmd.io/@jephianlin/SkWfW-5A2)
2. [Is this vector in the span? Case of no](https://hackmd.io/@jephianlin/B1cF4bcR2)
3. [Is this vector in the affine subspace? Case of yes](https://hackmd.io/@jephianlin/H1gJ8WcA3)
4. [Is this vector in the affine subspace? Case of no](https://hackmd.io/@jephianlin/ryX2qWq0h)
5. [Video: affine subspace](https://www.youtube.com/watch?v=-6wzNhJ-zeg&list=PLjjwN6s_CKYm_kZimbhEYfkQr8NmTiGqb&index=1)
6. [How to solve a system of linear equations?](https://hackmd.io/@jephianlin/HkM6o-cAh)
7. [Video: parametrize a system](https://www.youtube.com/watch?v=ZQ12ESNoy5k&list=PLjjwN6s_CKYm_kZimbhEYfkQr8NmTiGqb&index=2)
8. [Video: find particular and homogeneous solution](https://www.youtube.com/watch?v=uaMfAv8JX60&list=PLjjwN6s_CKYm_kZimbhEYfkQr8NmTiGqb&index=3)
9. [How to compare two sets?](https://hackmd.io/@jephianlin/r1UoWvxeT)
10. [How to compare two spans?](https://hackmd.io/@jephianlin/SJo19velp)
11. [Midterm 1: Questions to ponder](https://hackmd.io/@jephianlin/2023FMath103A-mid1) :star:
12. [SMART goals](https://hackmd.io/@jephianlin/S1QGXtzW6)
13. Vector space: [Hefferon](https://hefferon.net/linearalgebra/) Two.I.1
14. Subspace: [Hefferon](https://hefferon.net/linearalgebra/) Two.I.2
15. Kahoot! --- [Vector space](https://create.kahoot.it/share/vector-space/fdef79e2-9d2e-4889-9378-f6bbde1cd9a3)
16. Linear independence: [Hefferon](https://hefferon.net/linearalgebra/) Two.II
17. [Is this set linear independent? Case of yes](https://hackmd.io/@jephianlin/rJG8yk2zT)
18. [Is this set linear independent? Case of no](https://hackmd.io/@jephianlin/r1ysD1nfa)
19. [Linear independent or not?](https://hackmd.io/@jephianlin/S17hHoqGa)
20. [How to find a basis of the kernel?](https://hackmd.io/@jephianlin/SyPyuWrXT)
21. [How to find a basis of the row space?](https://hackmd.io/@jephianlin/rk5ARbS76)
22. [How to find a basis of the column space?](https://hackmd.io/@jephianlin/HJs0C-rQ6)
23. [Midterm 2: Questions to ponder](https://hackmd.io/@jephianlin/2023FMath103A-mid2) :star:
24. Vector representation: [Hefferon](https://hefferon.net/linearalgebra/) Two.III.1
25. Function: [Hefferon](https://hefferon.net/linearalgebra/) Appendix or [1121 la function basics](https://www.youtube.com/watch?v=ucmDPU3x2xA)
26. [Properties of a function](https://hackmd.io/@jephianlin/HJlRX3wNT)
27. Isomorphism: [Hefferon](https://hefferon.net/linearalgebra/) Three.I
28. [Is this function injective?](https://hackmd.io/@jephianlin/By5UCv7r6)
29. [Is this function surjective?](https://hackmd.io/@jephianlin/HkAYUdQHa)
30. Homomorphism (linear function): [Hefferon](https://hefferon.net/linearalgebra/) Three.II
31. [Matrix representation in $\mathbb{R}^n$](https://hackmd.io/@jephianlin/BkZ9m3FB6)
32. Matrix representation: [Hefferon](https://hefferon.net/linearalgebra/) Three.III
33. [Matrix is a price table](https://hackmd.io/@jephianlin/Hk1K2worT)
34. [Matrix representation in a vector space](https://hackmd.io/@jephianlin/SyV1wdiHa)
35. Change of basis [Hefferon](https://hefferon.net/linearalgebra/) Three.V
36. [Kernel and range of a linear function](https://hackmd.io/@jephianlin/r1xDsonS6)
37. [Final: Questions to ponder](https://hackmd.io/@jephianlin/2023FMath103A-final) :star:

:::info

The following terminologies are interchangeable:

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

## 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](https://www.youtube.com/watch?v=osEADxaIKIc)
- [Chapter 0: Essence of linear algebra preview](https://www.3blue1brown.com/lessons/eola-preview)
- Hefferon --- One.I.1

#### Week of 9/11

- [Chapter 1: Vectors, what even are they?](https://www.3blue1brown.com/lessons/vectors)
- Hefferon --- One.I.2 ~ 3

#### Week of 9/18

- [Chapter 2: Linear combinations, span, and basis vectors](https://www.3blue1brown.com/lessons/span)
- Hefferon --- One.II.1

#### Week of 9/25

- [Chapter 3: Linear transformations and matrices](https://www.3blue1brown.com/lessons/linear-transformations)
- Hefferon --- One.II.2 ~ III.2

#### Week of 10/2

- [Chapter 4: Matrix multiplication as composition](https://www.3blue1brown.com/lessons/matrix-multiplication)
- Hefferon --- Topic: Computer Algebra Systems

#### Week of 10/9

- [Chapter 5: Three-dimensional linear transformations](https://www.3blue1brown.com/lessons/3d-transformations)
- Hefferon --- Topic: Accuracy of Computations

### Linear spaces

#### Week of 10/16

- [Chapter 6: The determinant](https://www.3blue1brown.com/lessons/determinant)
- Hefferon --- Two.I.1 ~ 2

#### Week of 10/23

- [Chapter 7: Inverse matrices, column space and null space](https://www.3blue1brown.com/lessons/inverse-matrices)
- Hefferon --- Two.II.1

#### Week of 10/30

- [Chapter 8: Nonsquare matrices as transformations between dimensions](https://www.3blue1brown.com/lessons/nonsquare-matrices)
- Hefferon --- Two.III.1 ~ 2

#### Week of 11/6

- [Chapter 9: Dot products and duality](https://www.3blue1brown.com/lessons/dot-products)
- Hefferon --- Two.III.3 ~ 4

#### Week of 11/13

- [Chapter 10: Cross products](https://www.3blue1brown.com/lessons/cross-products)
- Hefferon --- Topic: Fields

### Linear functions

#### Week of 11/20

- [Chapter 11: Cross products in the light of linear transformations](https://www.3blue1brown.com/lessons/cross-products-extended)
- Hefferon --- Three.I.1 ~ II.1

#### Week of 11/27

- [Chapter 12: Cramer's rule, explained geometrically](https://www.3blue1brown.com/lessons/cramers-rule)
- Hefferon --- Three.II.2 ~ III.1

#### Week of 12/4

- [Chapter 13: Change of basis](https://www.3blue1brown.com/lessons/change-of-basis)
- Hefferon --- Three.III.2 ~ IV.3

#### Week of 12/11

- [Chapter 16: Abstract vector spaces](https://www.3blue1brown.com/lessons/abstract-vector-spaces)
- Hefferon --- Three.IV.4 ~ V.2

### More...

- [Chapter 14: Eigenvectors and eigenvalues](https://www.3blue1brown.com/lessons/eigenvalues)
- [Chapter 15: A quick trick for computing eigenvalues](https://www.3blue1brown.com/lessons/quick-eigen)
- Hefferon --- Three.VI.1 ~ 3
- Hefferon --- Topic: Line of Best Fit

## References

- Texkbook: [Linear Algebra](https://hefferon.net/linearalgebra/) by Jim Hefferon
- Texkbook: [Linear Algebra Done Right](https://linear.axler.net/) by Sheldon Axler
- YouTube playlist: [Essence of linear algebra](https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab) by 3Blue1Brown
- YouTube playlist: [Linear Algebra](https://youtube.com/playlist?list=PLO1y6V1SXjjN0auwro1YZEhhnM_yzsSzi) by The Math Sorcerer
- Online resource: [3Blue1Brown](https://www.3blue1brown.com/)
- Online resource: [LA Tea website](https://sagelabtw.github.io/LA-Tea/)
- Online resource: [Intuitive Math](https://intuitive-math.club/)
- Online resource: Khan Academy [Linear Algebra](https://www.khanacademy.org/math/linear-algebra)

## Linear Algebra from 3Blue1Brown

- [Chapter 0: Essence of linear algebra preview](https://www.3blue1brown.com/lessons/eola-preview)
- [Chapter 1: Vectors, what even are they?](https://www.3blue1brown.com/lessons/vectors)
- [Chapter 2: Linear combinations, span, and basis vectors](https://www.3blue1brown.com/lessons/span)
- [Chapter 3: Linear transformations and matrices](https://www.3blue1brown.com/lessons/linear-transformations)
- [Chapter 4: Matrix multiplication as composition](https://www.3blue1brown.com/lessons/matrix-multiplication)
- [Chapter 5: Three-dimensional linear transformations](https://www.3blue1brown.com/lessons/3d-transformations)
- [Chapter 6: The determinant](https://www.3blue1brown.com/lessons/determinant)
- [Chapter 7: Inverse matrices, column space and null space](https://www.3blue1brown.com/lessons/inverse-matrices)
- [Chapter 8: Nonsquare matrices as transformations between dimensions](https://www.3blue1brown.com/lessons/nonsquare-matrices)
- [Chapter 9: Dot products and duality](https://www.3blue1brown.com/lessons/dot-products)
- [Chapter 10: Cross products](https://www.3blue1brown.com/lessons/cross-products)
- [Chapter 11: Cross products in the light of linear transformations](https://www.3blue1brown.com/lessons/cross-products-extended)
- [Chapter 12: Cramer's rule, explained geometrically](https://www.3blue1brown.com/lessons/cramers-rule)
- [Chapter 13: Change of basis](https://www.3blue1brown.com/lessons/change-of-basis)
- [Chapter 14: Eigenvectors and eigenvalues](https://www.3blue1brown.com/lessons/eigenvalues)
- [Chapter 15: A quick trick for computing eigenvalues](https://www.3blue1brown.com/lessons/quick-eigen)
- [Chapter 16: Abstract vector spaces](https://www.3blue1brown.com/lessons/abstract-vector-spaces)