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Weekly Linear Algebra Full Course

SAT Score Range

25 sessions

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About

Discover the language of modern mathematics and science! In this weekly Linear Algebra course, you’ll build a solid foundation in vectors, matrices, and abstract vector spaces, and see how these ideas power everything from data science to physics and engineering.🏅✅💯️

Tutored by

Shijie(Allen) Z 🇺🇸

Certified in 2 topics

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Hi! I’m a high school junior from Wisconsin with a strong passion for mathematics and physics, and a proven track record of excellence. I earned perfect scores in AP Calculus BC, AP Statistics, and both AP Physics C: Mechanics and Electricity & Magnetism, and I’m currently challenging myself with advanced college-level math and physics courses. Beyond coursework, I have extensive experience in mathematics competitions, which have sharpened my problem-solving skills and deepened my love for creative, rigorous thinking. Teaching and sharing knowledge is one of my greatest joys — I love helping others understand difficult concepts and inspiring them to see the beauty in math. Joining Schoolhouse is an exciting step for me to help more students succeed, grow their confidence, and maybe even fall in love with math and physics like I did. Let’s learn together!

✋ ATTENDANCE POLICY

✅ Please make your best effort to attend each session live — your participation makes the class more interactive and fun for everyone!

✅ If you can’t make it to a session, no problem — just let me know when you can, and review the notes or recording (if provided) before the next class.

SESSION 1

16

Aug

SESSION 1

Other Topics

Other Topics

Sat 3:00 PM - 4:00 PM UTCAug 16, 3:00 PM - 4:00 PM UTC

Vectors & Geometry of ℝⁿ (Visualize vectors, length, angle, dot product)
SESSION 2

23

Aug

SESSION 2

Other Topics

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Sat 3:00 PM - 4:00 PM UTCAug 23, 3:00 PM - 4:00 PM UTC

Solving Linear Systems (Row‑reduction and echelon forms for Ax = b) ❌No Class Next Week
SESSION 3

6

Sep

SESSION 3

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Sat 3:00 PM - 4:00 PM UTCSep 6, 3:00 PM - 4:00 PM UTC

Matrix Algebra (Addition, multiplication, powers, block notation)
SESSION 4

13

Sep

SESSION 4

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Sat 3:00 PM - 4:00 PM UTCSep 13, 3:00 PM - 4:00 PM UTC

Matrix Inverses & Elementary Ops (Find A⁻¹, interpret row operations as matrices)
SESSION 5

20

Sep

SESSION 5

Other Topics

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Sat 3:00 PM - 4:00 PM UTCSep 20, 3:00 PM - 4:00 PM UTC

LU Decomposition Factor (A = LU for faster solving)
SESSION 6

27

Sep

SESSION 6

Other Topics

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Sat 3:00 PM - 4:00 PM UTCSep 27, 3:00 PM - 4:00 PM UTC

Determinants I (Cofactor expansion, geometric meaning)
SESSION 7

4

Oct

SESSION 7

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Sat 3:00 PM - 4:00 PM UTCOct 4, 3:00 PM - 4:00 PM UTC

Determinants II & Cramer’s Rule (Properties, multilinearity, applications)
SESSION 8

11

Oct

SESSION 8

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Sat 3:00 PM - 4:00 PM UTCOct 11, 3:00 PM - 4:00 PM UTC

Vector Spaces & Subspaces (Axioms; column space, null space examples)
SESSION 9

18

Oct

SESSION 9

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Sat 3:00 PM - 4:00 PM UTCOct 18, 3:00 PM - 4:00 PM UTC

Basis, Dimension & Rank (Linear independence tests; rank‑nullity theorem)
SESSION 10

25

Oct

SESSION 10

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Sat 3:00 PM - 4:00 PM UTCOct 25, 3:00 PM - 4:00 PM UTC

Coordinates & Change of Basis (Transition matrices; coordinates in new bases)
SESSION 11

1

Nov

SESSION 11

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Sat 3:00 PM - 4:00 PM UTCNov 1, 3:00 PM - 4:00 PM UTC

Linear Transformations (Kernel, image, matrix representation)
SESSION 12

8

Nov

SESSION 12

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Sat 4:00 PM - 5:00 PM UTCNov 8, 4:00 PM - 5:00 PM UTC

Eigenvalues & Eigenvectors I (Characteristic polynomial; eigen‑pairs)
SESSION 13

15

Nov

SESSION 13

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Sat 4:00 PM - 5:00 PM UTCNov 15, 4:00 PM - 5:00 PM UTC

Diagonalization (Conditions, repeated eigenvalues, powers of A) ❌ No Class Next and After Week
SESSION 14

6

Dec

SESSION 14

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Sat 4:00 PM - 5:00 PM UTCDec 6, 4:00 PM - 5:00 PM UTC

Complex Eigenvalues (Real vs. complex Jordan blocks; rotations)
SESSION 15

13

Dec

SESSION 15

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Sat 4:00 PM - 5:00 PM UTCDec 13, 4:00 PM - 5:00 PM UTC

Applications to ODEs (Solve x′ = Ax with eigen decomposition)
SESSION 16

20

Dec

SESSION 16

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Sat 4:00 PM - 5:00 PM UTCDec 20, 4:00 PM - 5:00 PM UTC

Mid‑Term Review & Problem Marathon (Cumulative practice, Q&A) ❌ No Class Next Week
SESSION 17

3

Jan

SESSION 17

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Sat 4:00 PM - 5:00 PM UTCJan 3, 4:00 PM - 5:00 PM UTC

Inner Products & Orthogonality (Norms, orthogonal sets, projections)
SESSION 18

10

Jan

SESSION 18

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Sat 4:00 PM - 5:00 PM UTCJan 10, 4:00 PM - 5:00 PM UTC

Gram‑Schmidt & QR Factorization (Orthonormal bases, least‑squares setup) ❌ No Class Next Week
SESSION 19

24

Jan

SESSION 19

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Sat 4:00 PM - 5:00 PM UTCJan 24, 4:00 PM - 5:00 PM UTC

Least‑Squares & Data Fitting (Normal equations, trend‑line example)
SESSION 20

31

Jan

SESSION 20

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Sat 4:00 PM - 5:00 PM UTCJan 31, 4:00 PM - 5:00 PM UTC

Symmetric Matrices & Spectral Thm. (Orthogonal diagonalization, real eigenbasis)
SESSION 21

7

Feb

SESSION 21

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Sat 4:00 PM - 5:00 PM UTCFeb 7, 4:00 PM - 5:00 PM UTC

Quadratic Forms & Definiteness (Classify surfaces; optimization criteria)
SESSION 22

14

Feb

SESSION 22

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Sat 4:00 PM - 5:00 PM UTCFeb 14, 4:00 PM - 5:00 PM UTC

Singular Value Decomposition I (Geometry of SVD; relation to rank)
SESSION 23

21

Feb

SESSION 23

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Sat 4:00 PM - 5:00 PM UTCFeb 21, 4:00 PM - 5:00 PM UTC

SVD Applications (Image compression demo; low‑rank approximation)
SESSION 24

28

Feb

SESSION 24

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Sat 4:00 PM - 5:00 PM UTCFeb 28, 4:00 PM - 5:00 PM UTC

Jordan Canonical Form (Intro) (When diagonalization fails; basic blocks)
SESSION 25

7

Mar

SESSION 25

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Sat 4:00 PM - 5:00 PM UTCMar 7, 4:00 PM - 5:00 PM UTC

Linear Dynamical Systems (Stability via eigen & Jordan analysis)

Public Discussion

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Aug 16 - Mar 7

30 weeks

60 mins

/ session

Next session on August 16, 2025

SCHEDULE

Saturdays

4:00PM