Linear Algebra 19b: Component Spaces - Doing It Right!

[srinsriram]

You hit on an important point. The limiting nature of cartesian bases which are promoted at the beginning of most texts (from high school). This prevents proper understanding and leads to forgetting the concepts. Your strategy of separating the 3 types of objects (geometric, polynomial functions, R^n) was something I find useful and effective in retaining the material.

[wawangsf]

Well said! The primary reason I chose to take these courses is because they treat objects on their own terms. Intuition leads to an understanding while methods of computation can always be derived from this understanding.

[GordonYiu]

I like your approach. Studying sets of numbers is very boring and keep me from appreciating the beauty of linear algebra. Knowing that it could handle so many different kinds of object makes me interested. I studied linear algebra 30 years ago and all I can remember is matrix operation. Now I study linear algebra again for my PhD program. These videos gives me even more fun than my professional subject. Thanks you very much.

[mhdalimoraly]

I could not agree more with Prof. Grinfeld's approach. The traditional way of teaching linear algebra is probably more suitable for mathematicians. On the other side in almost all other technical majors where Linear Algebra is used as a tool to solve real-world problems, you can strongly argue that Prof. Grinfeld's approach enables students to see the real connections between their field-of-study and these mathematical terms, even at the very early stages of studying linear algebra, instead of getting lost in a mathematical self-indulgent journey that will end up obscuring the beauty of the subject and getting many students frustrated. I hope that Prof. Grinfeld is considering writing a formal book that focuses on his treatment of linear algebra, and I hope that more undergraduate schools will be convinced to adapt his approach and safe many students from running away from mathematics.

[luisribeiro]

Your methodology helped me get a broader view on my independent study on computer vision which requires lots of understanding of multiple view geometry and which sits on linear algebra. Without having a broad view of spaces and distinctions of different contexts you are in, you end up dressing yourself like a clown without context!. Again, thank you very much for helping building my knowledge.

[elijahsmith]

This was a rude awakening in trying to learn about relativity as a math deficient hobbyist. I hope to return to relativity with a new perspective after completing this series. Thank you Prof Grinfeld. P.S. I also got your tensor book. Maybe one day...😂

[knivesoutcatchdamouse]

Very nice orthogonal lines at ~ 7:50!
👏👏👏

[swagatochatterjee]

No doubt I f-ing hated vector algebras in my post tenth grade Physics and Maths classes. They really started in with the wrong foot. Thanks for making me understand why I love Linear Algebra now but hated it back then.

[zkhandwala]

This is both fascinating and fantastic! My one question is this: what would/does Strang say in response?