Linear Algebra 3b4: Decomposition with Respect to Arbitrary Geometric Vectors, Affine Grid

[ektabansal]

this Linear algebra series along with the answered doubts in comments is more than what one can ask for

[souravdey]

This is most elegant video in all of liner algebra.

[IgorKuts]

Dear Prof., Thank you SO MUCH for taking the time to draw this grid! I was finally able to grasp the concepts of Affine Grids and Spaces all thanks to you!

I was watching you drawing the grid and then, out of the blue (for me), you started to write "AFFINE" on the blackboard ... a wide smile appeared on my face and it clicked for me. It was satisfactory moment, which I have never experienced, in connection to studying, before.

I am on the journey of conditioning myself to loving sciences and technical subjects.

[abdullahalsawalmeh]

, you explained the idea of Affine grid perfectly, Thank you

[antonellomascarello]

0:08 / 0:37 : IMPORTANT concept : span the entire plane
2:08 : Systematic Approach / 1st half of the grid
7:02 : 2nd half of the grid
8:41 : Not a Cartesian but an AFFINE Grid

[harrisondorn]

I didn't realize math could be so beautiful! :)

[kf]

Excellent, it all seems so much simpler now. Thanks for the explanation

[bernhardriemann]

I wish I could have given this video 5 likes

[martinsanchez-hwfi]

isn't affine when the grid is displaced from origin?

[alojzybabel]

Wouldn't it make much more sense to just draw a line parallel to b and passing through the tip of c to see where it will cut a?
And in the same way, draw a line parallel to a and passing through the tip of c to see where it cuts the line determined by b?

[tangolasher]

"Any 2 vectors that dont point in the same direction span the entire plane" - I think you made a mistake - isn't it "in the same, or OPPOSITE direction"?

[gostodeviralatas]

What happened professor, do you quit the course?

[aliensoup]

There is a marvelous invention that you might find useful called a 'straightedge'. Its made of wood and costs a couple dollars.