Thank you professor! I am amazed by the fact that professors from top institutes like MIT explain the mere basics without any expectation that we are supposed to know those topics earlier. On the other side our university professors just avoid the whole thing by saying "it isn't the part of syllabus, you are expected know this already". A huge salut and thanks to professor Strang and MIT team for publishing these videos free of cost.

The dot product of orthogonal vectors equals zero. All of a sudden it clicked when I remembered my conclusion as to what a dot product actually was, that is, "what amount of one vector goes in the direction of another." Basically, if vectors are orthogonal, then no amount of one will go in the direction of the other. Like how a tree casts no shadow at noon.

I really encourage you to buy The Introduction of Linear Algebra which Pf Strang wrote. If I say these videos are rank r, then I can definitely say the book is the orthogonal complement of these videos that makes perfect dimension of Linear Algebra.

"the origin of the world is right here"

That smile at the end, he knew he'd done a good job

Second best part about watching these lectures is the comment section

"blackboard extends to infinity..." yeah, MIT does have infinitely long blackboard...

Mr Strang makes me feel, in the first time of my life, that linear algebra is interesting!

To find this course on the web is tantamount to finding massive gold treasure.

i dont know how but when ever i need he repeats it.thx mr Strang

Gilbert Strang, you are truly an outstanding teacher! I am currently doing my Master's thesis in Finite Element Analysis and started watching these video lectures just for fun, since I already had some Linear Algebra back on my bachelor's. Your little sidenote at the end of a lecture about multiplying a system by A.transpose actually helped me crack a problem I'm dealing with right now. My finite element system had more equations than unknowns (because I'm fixing some internal degrees of freedom, not the nodes themselves) and I just couldn't figure out how to solve such system. I completely forgot about this trick of multiplying by a transpose!! THANK YOU SO MUCH!! My final system now has "good" dimensions and the stiffness matrix has a full rank!!!

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This lecture is a Tour of Force, every sentence he says, including the ancillary comments, are so well crafted that makes everything click with ease. Least Squares open the gates for the siamese fields of Optimization and Inverse Theory, so every bit of insight he shares has deep implications on those fields (and many others). It's not exaggeration to say that the whole lecture is an aha! moment. Very illuminating, thank you Professor Strang

okkkkk, cameras are rolling, this is lecture 14. What an intro line!

I have never felt the platonic injunction to "to carve nature at its joints" more strongly than after watching this lecture.

I remember falling asleep in all my linear algebra classes @ UWaterloo. Not until now that I'm starting to like linear algebra!

"Let me cook up a vector that's orthogonal to it" - the goat professor strang

In many linear algebra courses that I have seen, the student is simply told about the various relationships between the fundamental subspaces. But in this course these ideas are convincingly yet accessibly presented. This is very important because it allows students to really understand such key ideas of linear algebra to the point where they become intuitive, instead of simply memorizing properties and formulas. Another great lecture by professor Strang!

This series is phenomenal. Every lecture a gem. Thank you Mr Strang!

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