Linear Algebra Overview

By popular demand, in this video I'm presenting a non-technical overview of some of the main concepts in linear algebra, including systems of equations, matrices, vector spaces/bases, diagonalization, orthogonality, and least-squares. Hopefully it's understandable enough that you only need algebra to understand it. Also, of course I've skipped a couple of concepts as well, like linear transformations and determinants. Enjoy!

[david-ytoo]

YOU SHOULD MAKE A SERIES ON LINEAR ALGEBRA (I.E. IN DEPTH LINEAR ALGEBRA TO BE APPLIED LATER ON WITH DIFFERENTIAL EQUATIONS AND INTEGRATION!!)

[saitaro]

What you guys are doing is so valuable. This channel deserves it all.

[MrJapogm]

Linear Algebra was more delicious than the OMG burger.

[RodrigoCastroAngelo]

It's really good to see him so excited about algebra. Very inspirational.

[brendanlawlor]

WOW Dr Peyam your Linear Algebra reference to a product of 2 matrices being Zero 0 motivates eigenvalue treatment eg (A-I×ambda)=0 multiply by B so AB =B×lambda and then diag matrix follows when taking inverse B both sides.

The point is your motivation and simplicity educated me.
Didn't realise product of 2 matrices being 0 motivates the start wow now I see the basics.
Thx Dr Peyam your the best .
And also smiling / upbeat I like that too . Cheers Actuary Australia

[robertschlesinger]

Excellent overview of linear algebra that is well worth watching a couple of times. We are looking forward to more of your overviews and summaries.
Many thanks. [Mauti-shah-kiera! (sic). Sorry for any mistakes in the transliteration.]
Bob Schlesinger

[tomatrix]

I’m so hyped to enjoy your linear algebra

[staciemosier]

Just finishing my 1st term of linear algebra.... Thank you for helping me put such a seemingly random miasma of concepts into an ordered (linear) bigger picture!

[alanrodriguez]

Waoo! It's amazing. I would have liked a teacher to tell me a little "story" about linear algebra earlier to take classes on it, but now I am very grateful for you work on this video. Thank you very much!!!

[slavinojunepri]

This is a cool summary of linear algebra bringing back memories of wonderful concepts I learned in class so long ago.

[markkennedy]

Great overview. So many lecturers don't do this. Like when he comes to basis, for example, how he stresses how cool that concept is. Like a cadence in his lectures where he projects his own enthusiasm about what's important instead of reciting stuff. Anyway nice job

[drbob]

I believe in the Ax=0 example there is an error, as there is only x_3 free, and therefore s.[2 -1 0 2 1] is not a solution (e.g. setting s=1 yields [0 0 0 16]). Setting x_3 to 0 would only be useful if there were more than one free variable (otherwise it only generates the trivial zero solution). Love the video & enthusiasm, thanks for making it!

[PunmasterSTP]

Linear algebra overview? More like "So many things that you knew"...and were willing to share. Thank you so much!

[unknownful]

Have you ever wondered why Dr. Peyam is always covered in chalk?
Me too!
Some math mysteries are meant to be left unsolved...

[kingk.crimson]

This video was super helpful. I had to a semester gap between Linear Algebra 1 and 2 and I was worried I'd forget everything from 1 by the time I got to 2 but this was exactly what I needed. Thanks!!

Ah yes but WHAT is the Matrix, Neo?....

[seoexperimentations]

It s cool but mr peyam I am an undergrad in college and I m learning multivariable calculus and linear algebra and what connects these teo topics are determinants, like for the formula of the 2nd derivative test and the formula for jacobian you need to solve the determinant of a matric I would love if you could post a video explaining the power of determinants; how is it they re so usefull when we go in higher dimensions?!

[hartmutkern]

0:30 "of course i could talk for hours about it" please do so!

[Ajay-ibxk]

Thanks sir you gave us very best insight

[ericlizalde]

I'd like you go in more details or specific things, as you did in some other videos, not only in linear, also in calculus, analysis (maybe complex?) There are not so many channels on YouTube that go through those things and I'd like you to do it.
Thaanks! I like your videos