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Week

Monday

Wednesday

Video: Teaching Center!!!

1

Jan-18-2022

Jan-20-2022
0.1 First Meeting
[Notes #0.1]

2

Jan-25-2022
1.1 Intro to Linear Systems
[Notes #1.1] [with Supplements]
Movie(s):

• [Planes_01] (unique solution)
• [Planes-101] (Finding the unique solution)
• [Planes_02] (infinitely many solutions)
• [Planes-102] (Finding infinitely many solutions)
• [Planes_03] (no solution)
• [Planes-103] (Not finding any solutions)

Supplemental Material

• Metacognitive Reflection
• Row-reductions revisited
• Problem Statements for Suggested Problems
• ☛ Lab-1.1 ☚ (Labs are 101.3% experimental)

Quiz 1.1 — Due 11:59pm, Jan-28-2022

Jan-27-2022
1.2 Matrices, Vectors, and Gauss-Jordan Elimination
[Notes #1.2] [with Supplements]

Supplemental Material

• [Computer Science] perspective on a Matrix.
• Metacognitive Reflection
• Problem Statements for Suggested Problems
• ☛ Lab-1.2 ☚ (Labs are 101.3% experimental)

Recommended Video(s)

• [External] Essence of Linear Algebra
• Vectors, what even are they? (9:51)

Quiz 1.2 — Due 11:59pm, Jan-30-2022

3

Feb-01-2022
1.3 Solutions of Linear systems; Matrix Algebra
[Notes #1.3] [with Supplements]

Supplemental Material

• [Additional discussion] Statements (and contra-positive statements) regarding rank(A).
• Metacognitive Reflection
• Problem Statements for Suggested Problems

Quiz 1.3 — Due 11:59pm, Feb-04-2022

Schedule adjustment deadline.
(7:59 p.m. deadline, September 3rd)

Feb-03-2022
1.4 Matrix--Vector Fundamentals Wrapup
[Notes #1.4] [with Supplements]

Supplemental Material

• Metacognitive Reflection

Quiz 1.4 — Due 11:59pm, Feb-06-2022

4

Feb-08-2022
2.1 Linear Transformation and Their Inverses
[Notes #2.1] [with Supplements]
Movie(s):

• [LinTrans_01]
• [LinTrans_02]
• [LinTrans_03]
• [LinTrans_04]
• [LinTrans3d_01]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems

Quiz 2.1 — Due 11:59pm, Feb-11-2022

Feb-10-2022
2.2 Linear Transformations in Geometry
[Notes #2.2] [with Supplements]
Movie(s):

• [Rotation_2d]
• [Scaling_2d]
• [Projection_2d]
• [Reflection_2d]
• [Shear_2d]

Supplemental Material

• [Math] Challenge Question
• Metacognitive Reflection
• Problem Statements for Suggested Problems

Recommended Video(s)

• [External] Essence of Linear Algebra
• Linear transformations and matrices (10:58)

Quiz 2.2 — Due 11:59pm, Feb-13-2022

5

Feb-15-2022
2.3 Matrix Products
[Notes #2.3] [with Supplements]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems

Recommended Video(s)

• [External] Essence of Linear Algebra
• Matrix multiplication as composition (10:03)

Quiz 2.3 — Due 11:59pm, Feb-18-2022

Feb-17-2022
2.4 The Inverse of a Linear Transformation
[Notes #2.4] [with Supplements]

Supplemental Material

• Metacognitive Reflection
• "Live Math" (Fall 2019)
• Problem Statements for Suggested Problems

Quiz 2.4 — Due 11:59pm, Feb-20-2022

6

Feb-22-2022
Capstone Test #1 - Fundamentals (1.1 – 2.4)

Feb-24-2022
3.1 Image and Kernel of a Linear Transformation
[Notes #3.1] [with Supplements]
Movie(s):

• [exp(x)]
• [Unit Circle]
• [3D Loop]
• [LinTrans2D ex01(x)]
• [LinTrans2D ex02(x)]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems
• [Math] Bonus Proof and discussion — Properties of im(T)

Quiz 3.1 — Due 11:59pm, Feb-27-2022

7

Mar-01-2022
3.2 Subspaces of \( \mathbb{R}^{n} \); Bases and Linear Independence
[Notes #3.2] [with Supplements]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems

Quiz 3.2 — Due 11:59pm, Mar-04-2022

Mar-03-2022
3.3 The Dimension of a Subspace of \( \mathbb{R}^{n} \)
[Notes #3.3] [with Supplements]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems

Recommended Video(s)

• [External] Essence of Linear Algebra
• Linear combinations, span, and basis vectors (9:58)

Quiz 3.3 — Due 11:59pm, Mar-06-2022

8

Mar-08-2022
3.4 Coordinates
[Notes #3.4] [with Supplements]
Movie(s):

• [coord_movie]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems
• [Math] Beyond Vectors & Matrices — Linear Spaces

Quiz 3.4 — Due 11:59pm, Mar-11-2022

Mar-10-2022

Review

1.1 – 3.4

9

Mar-15-2022

Capstone #1 Solutions

Mar-17-2022
Capstone Test #2 - Subspaces (3.1 – 3.4)

10

Mar-22-2022
5.1 Orthogonal Projections and Orthonormal Bases
[Notes #5.1] [with Supplements]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems
• [Application] The (Fast) Fourier Transform
• [Application] MPEG-4 Video Compression

Quiz 5.1 — Due 11:59pm, Mar-25-2022

Mar-24-2022
5.2 Gram-Schmidt Process and QR Factorization
[Notes #5.2] [with Supplements]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems
• [Application] Solving the "Unsolvable" (Keywords: Minimum Residual, Least Squares, Linear Regression)
• [Problem] V = { x₁ + x₂ + x₃ + x₄ = 0 }
• [Problem] Gram-Schmidt and QR-facorization

Quiz 5.2 — Due 11:59pm, Mar-27-2022

Video: Linear Algebra meets Calculus: visualization of a tangent plane (in multiple locations) of a surface.

-

Mar-29-2022

Spring Break

Mar-31-2022

Spring Break

11

Apr-05-2022
5.3 Orthogonal Transformations and Orthogonal Matrices
[Notes #5.3] [with Supplements]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems
• [Application] Least Squares Data Fitting;
• [Math] Bonus Theory and Proofs — Orthongonal Transformations and Orthonormal Bases; Linear Spaces; ker(A^TA), ker(A), invertibility of (A^TA)

Quiz 5.3 — Due 11:59pm, Apr-08-2022

Apr-07-2022

Review

5.1 – 5.3 Orthogonal Projections, Orthonormal Bases, Gram-Schmidt, QR-Factorization, Orthogonal Transformations, and Orthogonal Matrices

12

Apr-12-2022

Capstone #2 Solutions

Apr-14-2022
Capstone Test #3 - Orthogonality (5.1 – 5.3)

13

Apr-19-2022
6.1 Determinants :: Executive Summary
[Notes #6.1] [with Supplements]
Movie(s):

• [Cross_Dot]

Supplemental Material

• Metacognitive Reflection
• Problem Statements for Suggested Problems
• [Example] 5-by-5 determinant by Laplace co-factor expansion
• [Example] 5-by-5 determinant by row reduction to upper triangular matrix
• [Math] "Proof" Linearity of the determinant in the columns
• [Math] The 7D Cross Product, Quarternions, Octonions, and other nonsense!
• [Math] "Proof" Determinants of Products and Powers
• [Math] ODE example: Variation of Parameters
• [Cut] "Pattern" / Combinatorial definition of the Determinant
• [Cut/Example] Computation of det(A) for a 4×4 matrix with many zeros (sparse matrix) using the combinatorial (pattern) method.
• [Cut] Determinants of Block Matrices
• [Discussion] Computational Feasibility of the Determinant (using the "pattern" or Laplace co-factor expansion methods)

Quiz 6.1 — Due 11:59pm, Apr-22-2022

Apr-21-2022
7.1 Diagonalization
[Notes #7.1] [with Supplements]
Movie(s):

• [Tacoma Narrows] (YouTube)
• [A²⁰⁰ movie]
• [A_3d²⁰⁰ movie]
• [KS_hopping_3]
• [KS_hopping_4-10]

Supplemental Material

• Problem Statements for Suggested Problems
• Complex Analysis: Essentials for Linear Algebrax

Quiz 7.1 — Due 11:59pm, Apr-24-2022

14

Apr-26-2022
7.2 Finding Eigenvalues of a Matrix
[Notes #7.2] [with Supplements]

Supplemental Material

• Problem Statements for Suggested Problems
• Complex Eigenvalues

Quiz 7.2 — Due 11:59pm, Apr-29-2022

Apr-28-2022
7.3 Finding Eigenvectors of a Matrix
[Notes #7.3] [with Supplements]

Supplemental Material

• Problem Statements for Suggested Problems
• Complex Eigenvectors, Complex Diagonalization, Block-Diagonalization

Quiz 7.3 — Due 11:59pm, May-01-2022

15

May-03-2022
7.E Diagonalization, Finding Eigenvalues and Eigenvectors of a Matrix
[Notes #7.E]

May-05-2022

Capstone #3 Solutions

16

May-10-2022

FINALS WEEK

May-12-2022

8:00am – 10:00am

Capstone Test #4 - Eigenvalues and Eigenvectors (7.1 – 7.E)

Mandatory (WeBWork) Homework will be assigned.

HIGHLY "Recommended" Problems

• Topic 1 : Linear Systems
  • 1.1 — 1, 3, 7, 14, 19, 21, 42
  • 1.2 — 1, 3, 9, 11, 18, 21, 34
  • 1.3 — 1, 2, 3, 7, 13, 22, 23, 37, 46, 55
• Topic 2 : Linear Transformations
  • 2.1 — 1, 2, 3, 4, 5, 7, 8, 13, 14, 16, 17, 41, 42
  • 2.2 — 1, 6, 7, 9, 12, 13, 17, 26
  • 2.3 — 1, 3, 5, 7, 13, 17, 19, 27, 28, 33, 37
  • 2.4 — 1, 3, 9, 16, 17, 29, 31, 35
• Topic 3 : Subspaces of Rⁿ
  • 3.1 — 1, 7, 11, 14, 15, 17, 23, 24, 29, 39
  • 3.2 — 1, 3, 7, 11, 17, 25, 27, 32, 34
  • 3.3 — 1, 3, 19, 23, 25, 27
  • 3.4 — 1, 3, 7, 17, 19, 23, 37
• (Topic 4 : Linear Spaces (Generalization)) — Partially "Absorbed" into the other topics, and fully addressed in Math 524
  • 4.1 — 1, 3, 5, 6, 8, 17, 20, 25, 32, 37
  • 4.2 — 1, 9, 13, 17, 18, 33, 51, 53, 63
  • 4.3 — 1, 5, 7, 9, 13, 15, 21, 25, 37, 41, 51, 55, 61
• Topic 5 : Orthogonality, Gram-Schmidt, and QR-Factorization
  • 5.1 — 7, 10, 11, 15, 17, 27, 28
  • 5.2 — 3, 7, 13, 31, 32, 33, 35, 39
  • 5.3 — 1, 2, 5, 6, 13, 15, 17, 19, 28, 32, 33, 36, 41
• Topic 6 : Determinants (A Minimal Introductions)
  • 6.1 — 1, 5, 11, 13, 23, 25, 27, 31, 43, 45
  • 6.2 — 1, 5, 7, 9, 11, 12, 13, 15
  • 6.3 — 1, 3, 5, 7, 9, 11, 13, 19-20-21
• Topic 7 : Eigenvalue and Eigenvectors
  • 7.1 — 1, 3, 5, 7, 15, 17, 21
  • 7.2 — 1, 3, 5, 11, 15, 17, 19, 23
  • 7.3 — 1, 3, 5, 9, 13, 17, 23, 27, 31, 35
  • (7.4 — 1, 5, 11, 25, 35, 37, 39, 41, 43, 47)
  • (7.5 — 13, 15, 17, 21, 23)