# Linear Algebra – Full College Course

September 1, 2024 2024-09-01 19:11## Linear Algebra – Full College Course

Learn Linear Algebra in this 20-hour college course. Watch the second half here: https://youtu.be/DJ6YwBN7Ya8

This course is taught by Dr. Jim Hefferon, a professor of mathematics at St Michael’s College.

📔 The course follows along with Dr. Hefferon’s Linear Algebra text book. The book is available for free: http://joshua.smcvt.edu/linearalgebra/book.pdf

📚 Access additional course resources at: https://hefferon.net/linearalgebra/

🔗 Stephen Chew’s Learning How to Learn series: https://www.youtube.com/watch?v=htv6eap1-_M&list=PL85708E6EA236E3DB

🔗 3Blue1Brown’s Linear Algebra series: https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

⭐️ Course Contents ⭐️

⌨️ (0:00:00) Introduction to Linear Algebra by Hefferon

⌨️ (0:04:35) One.I.1 Solving Linear Systems, Part One

⌨️ (0:26:08) One.I.1 Solving Linear Systems, Part Two

⌨️ (0:40:56) One.I.2 Describing Solution Sets, Part One

⌨️ (0:54:21) One.I.2 Describing Solution Sets, Part Two

⌨️ (1:02:48) One.I.3 General = Particular + Homogeneous

⌨️ (1:18:33) One.II.1 Vectors in Space

⌨️ (1:35:08) One.II.2 Vector Length and Angle Measure

⌨️ (1:51:31) One.III.1 Gauss-Jordan Elimination

⌨️ (2:00:00) One.III.2 The Linear Combination Lemma

⌨️ (2:44:32) Two.I.1 Vector Spaces, Part One

⌨️ (3:08:12) Two.I.1 Vector Spaces, Part Two

⌨️ (3:33:01) Two.I.2 Subspaces, Part One

⌨️ (3:58:16) Two.I.2 Subspaces, Part Two

⌨️ (4:23:43) Two.II.1 Linear Independence, Part One

⌨️ (4:45:11) Two.II.1 Linear Independence, Part Two

⌨️ (5:03:57) Two.III.1 Basis, Part One

⌨️ (5:23:55) Two.III.1 Basis, Part Two

⌨️ (5:42:34) Two.III.2 Dimension

⌨️ (6:03:24) Two.III.3 Vector Spaces and Linear Systems

⌨️ (6:25:09) Three.I.1 Isomorphism, Part One

⌨️ (6:54:08) Three.I.1 Isomorphism, Part Two

⌨️ (7:21:47) Three.I.2 Dimension Characterizes Isomorphism

⌨️ (7:43:43) Three.II.1 Homomorphism, Part One

⌨️ (8:14:52) Three.II.1 Homomorphism, Part Two

⌨️ (8:30:24) Three.II.2 Range Space and Null Space, Part One

⌨️ (9:00:17) Three.II.2 Range Space and Null Space, Part Two.

⌨️ (9:20:57) Three.II Extra Transformations of the Plane

⌨️ (9:52:06) Three.III.1 Representing Linear Maps, Part One.

⌨️ (10:13:18) Three.III.1 Representing Linear Maps, Part Two

⌨️ (10:34:18) Three.III.2 Any Matrix Represents a Linear Map

⌨️ (10:58:32) Three.IV.1 Sums and Scalar Products of Matrices

⌨️ (11:19:14) Three.IV.2 Matrix Multiplication, Part One

⌨️ Three.IV.2 Matrix Multiplication, Part Two (We accidentally left this section out. Watch it here: https://youtu.be/aWubyx5bBn4)

The following sections are in the second video: https://youtu.be/DJ6YwBN7Ya8

⌨️ Three.IV.3 Mechanics of Matrix Multiplication

⌨️ Three.IV.4 Matrix Inverse, Part One

⌨️ Three.IV.4 Matrix Inverse, Part Two

⌨️ Three.V.1 Changing Vector Representations

⌨️ Three.V.2 Changing Map Representations, Part One

⌨️ Three.V.2 Changing Map Representations, Part Two

⌨️ Three.VI Projection

⌨️ Four.I.1 Determinants

⌨️ Four.I.3 Permutation Expansion, Part One

⌨️ Four.I.3 Permutation Expansion, Part Two

⌨️ Four.I.4 Determinants Exist (optional)

⌨️ Four.II.1 Geometry of Determinants

⌨️ Four.III.1 Laplace’s formula for the determinant

⌨️ Five.I.1 Complex Vector Spaces

⌨️ Five.II.1 Similarity

⌨️ Five.II.2 Diagonalizability

⌨️ Five.II.3 Eigenvalues and Eigenvectors, Part One

⌨️ Five.II.3 Eigenvalues and Eigenvectors, Part Two

⌨️ Five.II.3 Geometry of Eigenvalues and Eigenvectors

—

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## Comments (50)

## @emperor8716

Lost me at the 12th minute 😂

## @michellepark0954

Thank you so much ill do this almost daily if i can ♡ i wanted to get into linear algebra but had no idea where to start as im not a mathematics major and was overwhelmed by it but this helps a lot

## @gamingtitan0

This has to be the most confusing course I ever watched.

I have to go look for external videos for every topic he discussed so I can understand them

## @RishiSrivastavaIIITD

16:12 😅😂

## @davidehrlich4138

Are there any math courses I need to take that are necessary to understand linear algebra

## @akhileshakhil4390

I am planning to become an AI/ML engineer and need guidance on where to start with Linear Algebra. Does this playlist cover all necessary Linear Algebra topics for AI/ML? Does it include any material not required for this field? Can I rely solely on this resource for my learning needs? Detailed answers would be greatly appreciated. Thank you.

## @user-iq6zm3fw5y

i have an exam in vector algebra tomorrow and i havn't open the book in past three years😂

wish me good luck😢

## @ramstudypoint7252

Nice

## @KingArshSingh

Did you guys solve all the problems in exercises or just the ones on topics he covered in the lectures?

## @aurora_rose

PROGRESS — 1:40:00

## @eliotargy1

I understood everything at the first time of watching. This has NEVER happened before.

## @wackywally69420

thank you, i had a terrible professor that nearly ruined this beautiful topic for me, by treating it like theres only one way to study or understand and only HIS way.

## @muhammadusmangillani823

Me after 11 hours😮😮😮

## @BMiller-qh5js

For those of us who are doing self-study, Linear Algebra is not General Algebra. Complete Algebra 1 & 2, as well as Calculus 1 before attempting this course.

## @adelinadonisa

Is this helpful if I want to change my career and dive into Python , AI and Data Analysis?

## @biswajitghosh3136

What is the best book to learn linear algebra

## @jackschleich9475

do you have a pure programming or algorithm version? I like going back and understanding the equations when necessary, but I'm trying to get the math into the computer as much as possible.

## @frenchmike

26:08

## @UDAYKIRAN_

Does this course is applicable for Machine Learning and data science?

## @msg-1995

3:40:25

## @rakib17874

Thank you so much for your incredible efforts and all the knowledge you are pouring freely ..

Big Hug🥰🥰🥰

## @vinaybanka3601

Can anyone tell me that this is also for Machine learning?

## @motivationda2067

man looks like lizard villain scientist in the amazing spider man

## @shin-ishikiri-no

Is it standard notation to represent rows with "P" instead of "R"? It seems to depend on the person teaching… I also noticed you didn't use the matrix format when converting to REF.

## @Lereya

I just wanted to say thank you so much for making this so readily available. I'm 40, and I want to enhance my retention and generally brush up on things that I haven't encountered in over 20 years. I deeply appreciate you making these videos, and making the textbook freely available. Knowledge should be free. I know that this is a huge effort, and I just wanted to say, from the bottom of my heart, thank you so much for your academic service to the learning public.

## @ravalik2103

Is these course useful for gate exam

## @rachetbomb9064

Part 2 [07:50:28 video length]: https://youtu.be/DJ6YwBN7Ya8

## @1o2red

Random urge to watch a 11 hour video on linear algebra

## @jorgegonzalez4720

Jim Hefferon seems like an absolutely wonderful human being

## @introvertdiaries4705

where are the answers for the problems in text book?

## @sudipseth8708

Just realized that first 5 minutes is the most important, and we all should apply it, to take this course effectively.

## @azi2047

My exams are tomorrow. Let's do this.

## @carlosrios6334

My God, what I would've given to have a math teacher like when I was in school and in college… your way of teaching is so motivating!!! Thank you so much for your time and dedication on this!

## @ayurilimje7469

Can I use this course for learning required for Data Science?

## @giwrgosok9616

Good lesson thanks for sharing.

## @jesusesteban1014

Could you activate the captions?😢

## @unompenumevrafalsy1914

mann.. you americans do linear algebra different then europeans

## @anshiscool

Hello!

## @Boltkiller96

8:34

## @TizianoMontenegro07

Thank you so much 🎉

## @DemiHalf

Shouldn't page 197 ex 1.29 say inverse image instead of image? or change the solution; changing x to x/2 and y to y/3 won't make the circle smaller.

## @Bedoroski

Mad respect for all of this work, not to mention the advice section

## @varunahlawat9013

Damn!

## @IgorBojanic-qr6fr

Hello hi hi

## @daveb970

why not use matrices @15 mins?

## @nonentity168

"The problem isn't hard itself, the hard part is to know what you're asked to do".

Gonna live with this quote now

## @stoopsartsunlimited

Halp.

I understand that the exercises come with solutions, so that I can check my work. Where can I find them?

It would be really helpful if the textbook's table of contents listed the exercises and solutions, especially because that's the primary reason I have the book.

## @codemathlab

Wow, This is so great that a course like this is free online. This is far better than my university lectures.

## @user-gz6tb9kw3l

Sir,Awesome class.from Bangladesh

## @erickraus7953

Hi, hi, hello!