Independence, Basis, and Dimension

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
Instructor: Gilbert Strang

Vectors are a basis for a subspace if their combinations span the whole subspace and are independent: no basis vector is a combination of the others. Dimension = number of basis vectors.

License: Creative Commons BY-NC-SA

[valeriereid]

I am certainly glad to see a professor who teaches from his brain, not reading from power point slides. This is refreshing.

[jmr]

Wow, the first 2 minutes of this lecture explain the topics better than 1.5 hours listening to my current teachers.

[SilverArro]

All math and engineering majors should be required to learn Linear Algebra from Dr. Strang. His lectures are beautiful, crystal clear, and emphasize the big ideas of the subject, and how they connect to one another.

[cristinabosch]

GILBERT STRANG, YOU ARE A GIFT FROM THE I HAD NOT UNDERSTOOD ANY LINEAR ALGEBRA WITH MY LECTURER AND YOU ARE NOW SAVING MY LIFE!!! YOU ARE B E A U T I F U L, thanks for changing my life 😩😩😩😩

[divutiful]

It's a treat to the brain. He is explaining like a person does not know anything about the topic but still can go through the lecture. Hats off to the professor here.

[andrescm]

Man... Wish my linear Algebra classes were as half as good as this one...
This is simply beautiful.

[water]

This dude wrote the text book im referring for linear algebra! His lectures are as amazing as his book!

[rickeyaustin]

First video in the series Dr. Strang did not start with "Okay!". I love the work he has done and his effort to provide quality teaching to the world! Thank you!

[ragsiruh]

A beautiful lecture! For the first time I understand basic terminology of Linear Algebra! Phew! There's a special place in heaven for you. There's a reason why MIT is MIT

[johnxiaoyuzhang]

I am glad people like me who did not get into MIT can take MIT courses. All the videos I saw from MIT are very clear, easy to follow, and well-structured! amazing

[vongxiong]

1, 0, 0 is a better A3... then.. that loser, that 6, 3, 5.
LOL he's halarious.

[jwyliecullick]

This lecture series shows vast improvement over previous eras; its total lack of fluff, jokes, anecdotes, it's just non-stop content in a nice little 13 minute package. I'm reviewing in the background, it's a great refresher even if oriented towards new students.

[farrugiamarc]

It is amazing how Professor Gilbert Strang manages to explain such an abstract mathematical topic with so much detail, yet making it easy to understand. He has all the qualities of a good teacher.

[stalins]

You are amazing sir... Education is all about transferring your intuition to others... You always great in that.

[alvinaawan]

You are a life saver, huge respect for the way you teach. Finally I understood all of the concepts after struggling for about one year. Hatsoff. Thankyou so much Sir

[LICHKINGShow]

Thank the lord for this man. My teacher can't teach in a way that makes sense for his students, but Dr. Strang made it all make sense.

[lightcapmath]

Am reviewing LA and have not done it in over 20 years. This first lecture of Dr.S, as many have commented, is very clear and simple. Thank you Dr. S DVD:)

[souvikcseiitk]

First 2 minutes of the video are more than sufficient to kick off any vector space problem you'll ever face in exams. Thanks for preserving quality education, I am really fed up with brainless professors these days trying to print formulas in brain. Thanks MIT and IIT for preserving quality education

[funghang]

professor like Dr strang produces brilliant student, and the student are the reputation of the university . 20 lecture of my professor= 13 min lecture of Dr strang .

[vocdex]

Thanks to Dr Strang, I can now visualize what does all concepts represent. The things are very clear right now.