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!