New linear algebra video coming soon...

Nice

Honestly I just finished Matrix Theory...and the book was kind of terrible. Now I have an awesome appreciation for what this has enabled us to do computationally. I also had no idea how huge of a badass Roger Penrose is. I watched your linear videos to review during this course. They are good. Aside from your channel, looking for content past basic Linear Algebra I found not much. The MIT open courseware Linear Algebra class is good but doesn't go much past. There are VERY few vids on: finding Jordan Cannonical Form, finding uglier matrix pseudo inverses, problems using sets of arbitrary vector proofs, implications of symmetry/skew/hermitian etc. theoretically. More power to you... that content is definitely lacking online, if you were by chance interested.

Hmm, it's not in the current plans. It could be worth it to talk about quadratic forms, but I don't know how high a priority that is. What do you ask?

3blue1brown

Hi Grant, Do you plan to make a video about positive definite matrices?

Raphael doesn't that get into a bit more Real Analysis? I wasn't familiar with it popping up in an algebra setting (but could be totally wrong). I would LOVE to see an essense of Real Analysis, or essense of Group Theory, or essense of Cryptography.

Shel Hammer

Thanks so much! I think this is a fantastic project.

Programmable Spacecraft

Also, for suggestions for more linear algebra videos: I would recommend eventually doing something about norms and thus metrics. It would be a great transition to a more analysis focused series, and would allow you to talk more in depth about sequences and limits

Zairaner

I admit it, I wasn't too happy when you/the people decided that you will do probability next. Mainly subjective of course-probability being my last favourite part of maths- but also some objective concerns, mainly me not being able to see how your approach, your geometric approach, would work with probability, except you would also do a lot of measure theory, and of course probability being the one thing that leads to nothing else, does not enable you to talk about some other, more in depth topic like topology, analysis or more algebra would have done. So seeing a new linear algebra topic makes me a lot more happy than most probability videos would do, and I really hope probability is not keeping you from doing things that would interest you more, especially while you do not really enjoy doing probability.

Zairaner

It's on the list!

3blue1brown

I will be extremely grateful if you guys could make a video about the geometric properties and interpretation of the transpose operation, and specifically what is the geometric intuition for why row rank is equal to column rank. I really interested to grasp better understanding... I believe many others as well. Here is an example for the popularity of this subject: <a href="https://math.stackexchange.com/questions/332908/looking-for-an-intuitive-explanation-why-the-row-rank-is-equal-to-the-column-ran" rel="nofollow noopener" target="_blank">https://math.stackexchange.com/questions/332908/looking-for-an-intuitive-explanation-why-the-row-rank-is-equal-to-the-column-ran</a> Keep up good work! I love what you're doing.

Some will be filling in gaps I see in the original series. For example, this on addresses actually solving systems of linear equations rather than just entirely letting the computer be a blackbox. It's not the most efficient algorithm, and it's not meant to be practical in that way, but I do think having deeper understandings for why certain computational methods works can strengthen your muscles with the subject. Likewise, discussing the transpose matrix is a gap I see in the original. Much will also be new and moving forward, like building up to SVD and PCA. I may also have some on what looks different for vector spaces over the complex numbers (as is highly relevant for quantum).

3blue1brown

This is exciting!

Vincent Zalzal

So lucky to live with 3B1B

So excited! I'd also be interested in digging into a little bit of group theory!

Thanks so much Grant! I'm taking a linear algebra course right now, and to prep, I watched through your original series a month ago. Absolutely fantastic, and it has given me such a good starting point to start understanding this stuff. Can't wait to see the extension video!

Alex Loftus

" an extension to the linear algebra" The Geometric Algebra?! (please)

Job van der Zwan

can't wait! appreciate all our efforts!

Generally, what will the new videos be about?

Looking forward to it!

How could we complain, when you're giving us great content; whether it's "Essence of" series or standalones? But I'm not going to lie; I am eager to see the extension series.

Magnasium

The timing couldn't have been better for me !!