Advanced Linear Algebra - Lecture 1: What is a Vector Space?

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In this lecture, we learn what a vector space is and we see some of the standard examples including R^n, the set of real-valued functions, and the set of matrices.

Please leave a comment below if you have any questions, comments, or corrections.

Corrections:
- Of course, the very first thing I say in this entire lecture series is wrong. This course is MATH 3221 at Mount Allison, not MATH 3211.

Timestamps:
00:00 - Introduction
8:27 - Vector spaces
16:50 - R^n
21:35 - Function space
26:12 - Matrix space
28:08 - A weird vector space
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I came from r/math, and I am still in shock by the perfect timing of this playlist. My Advance Linear Algebra course started a week ago, so this playlist is going to be a huge help! Thank you so much for your effort, us students appreciate great professors like you!

iak
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I've been taking the Strang 18.06 at MIT and the 18.06 lectures are very good. But Johnston's two courses are excellent also. Johnston emphasizes different things and brings different things together. He compliments Strang, and fills in important gaps. Highly recommend this Johnston course. A real contribution. Artfully taught. Love the pace of speaking..

PaulNielan
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Everything is explained in such an intuitive down to earth manner abstract things become straightforward very quickly. This is excellent.

strippins
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Here from your post on reddit, thank you for doing this course!

atomiccompiler
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Simply Superb. Clear, Efficient, and Engaging.

srinsriram
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Seems comprehensive and nice structured. Gonna watch all. Thanks for your effort!

nazmbicer
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Love the energy and the way you explained it all.

Bargainsxx
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One minor suggestion I would make, and you've likely spotted this already, is to beware having your webcam obscuring what we're supposed to be looking at. For example, from 35:45 the line of text you're talking about disappears behind you so we can't see it. Maybe it's obvious enough in this case but it might not have been.

PhilBoswell
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Also here from Reddit. Thank you so much for sharing! I just started adv. lin alg class (using Axler's book) and I'm so excited to have a second explanation throughout the course.

whitneyholman
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It seems to me that I learnt more about Linear Algebra as he was summarizing the previous course, than I did actually taking such a course.

Sidionian
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Congrats on building this book and video content! This looks excellent, I'm gonna go buy this book.

AxiomTutor
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Super nice stuff! I need to brush up on my elementary linear algebra before watching these though lol. Thanks for making these.

brendanchamberlain
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This is fantastic for quantum computing.

vorpalinferno
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does this course explain hessian matrix anywhere?

PerfectGuyHere
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question, do you have a basic linear algebra playlist

maxpercer
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do you have any videos made for math 2221?

jaaasoonedyyytts
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Sir, just take my subscription damn it.

rrt
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In our class the basic Linear Algebra is this Advanced Linear Algebra :/

samuelfisher