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Linear Algebra 101 From a 🎓 Stanford Math/Physics Major

SAT Score Range

•

11 sessions

✨ Be the first

About

👋Welcome to my Linear Algebra 101 Series!

❗This course will take you through a 12-session, college-level fundamental introduction to Linear Algebra: Vectors, Spaces, Matricies, Transformations, Eigenstuff, Applications, and more.

I look forward to working with all of you!

Tutored by

Jasper S 🇺🇸

Certified in 7 topics

View Profile

hi! my name is jasper :) i love math, physics, and spreading knowledge and positivity ^_^

Schedule

✋ ATTENDANCE POLICY

This course is cummulative, so each session adds new information that is vital to build a full understanding of Linear Algebra. I ask that you try not to miss more than two subsequent sessions, and always let me know beforehand if you need to be absent!

SESSION 1

26

Aug

SESSION 1

Other Topics

Other Topics

Tue 9:30 PM - 11:00 PM UTCAug 26, 9:30 PM - 11:00 PM UTC

Session 1: Introduction to Vectors and Vector Spaces

- Scalars vs. vectors
- Vector addition, scalar multiplication
- ℝⁿ and general vector spaces
- Axioms of vector spaces
- Examples: ℝ², ℝ³, function spaces, etc.


SESSION 2

29

Aug

SESSION 2

Other Topics

Other Topics

Fri 9:30 PM - 11:00 PM UTCAug 29, 9:30 PM - 11:00 PM UTC

Session 2: Subspaces

- Definition of Subspaces
- Zero subspace, lines, and planes through origin
- Span and linear combinations
- Visual intuition in 2D/3D
- Introduction to null space and column space
SESSION 3

2

Sep

SESSION 3

Other Topics

Other Topics

Tue 9:30 PM - 11:00 PM UTCSep 2, 9:30 PM - 11:00 PM UTC

Session 3: Linear Systems and Row Reduction

- Systems of linear equations
- Augmented matrix and elementary row operations
- Reduced row echelon form
- Gaussian, Gauss-Jordan elimination


SESSION 4

5

Sep

SESSION 4

Other Topics

Other Topics

Fri 9:30 PM - 11:00 PM UTCSep 5, 9:30 PM - 11:00 PM UTC

Session 4: Rank and Consistency

- Rank
- Consistency
- Homogeneity
- Solutions: unique, infinite, none

SESSION 5

9

Sep

SESSION 5

Other Topics

Other Topics

Tue 9:30 PM - 11:00 PM UTCSep 9, 9:30 PM - 11:00 PM UTC

Session 5: Linear Transformations

- Definition
- Matrix representations
- Domain, codomain, image
- Geometric interpretation: rotations, reflections, projections
SESSION 6

12

Sep

SESSION 6

Other Topics

Other Topics

Fri 9:30 PM - 11:00 PM UTCSep 12, 9:30 PM - 11:00 PM UTC

Session 6: Matrix Algebra

- Matrix addition, multiplication
- Transpose, identity, inverse
- Composition of transformations
- Matrix powers and algebraic properties
SESSION 7

16

Sep

SESSION 7

Other Topics

Other Topics

Tue 9:30 PM - 11:00 PM UTCSep 16, 9:30 PM - 11:00 PM UTC

Session 7: Basis and Dimension

- Linear independence
- Standard basis in ℝⁿ
- Dimension
SESSION 8

19

Sep

SESSION 8

Other Topics

Other Topics

Fri 9:30 PM - 11:00 PM UTCSep 19, 9:30 PM - 11:00 PM UTC

Session 8: Coordinates and Change of Basis

- Coordinates relative to a basis
- Transition matrices
- Changing representations
- Practical computations
SESSION 9

23

Sep

SESSION 9

Other Topics

Other Topics

Tue 9:30 PM - 11:00 PM UTCSep 23, 9:30 PM - 11:00 PM UTC

Session 9: Eigenvalues and Eigenvectors

- Definitions
- Diagonalization
- Characteristic polynomial
- Computing eigenvalues and eigenvectors
SESSION 10

26

Sep

SESSION 10

Other Topics

Other Topics

Fri 9:30 PM - 11:00 PM UTCSep 26, 9:30 PM - 11:00 PM UTC

Session 10: Applications

- Diagonalization for matrix powers
- Markov chains, population models
- Vibration modes and stability analysis
- Differential equations
SESSION 11

30

Sep

SESSION 11

Other Topics

Other Topics

Tue 9:30 PM - 11:00 PM UTCSep 30, 9:30 PM - 11:00 PM UTC

Session 11: Inner Product and Orthogonality

- Dot product, inner product space
- Orthogonal and orthonormal sets
- Gram-Schmidt process
- Projections onto subspaces

Public Discussion

Please log in to see discussion on this series.

Aug 26 - Sep 30

6 weeks

90 mins

/ session

Next session on August 26, 2025

SCHEDULE

Tuesdays

9:30PM

Fridays

9:30PM