Projection into Subspaces

MIT 18.06SC Linear Algebra, Fall 2011
Instructor: Nikola Kamburov

A teaching assistant works through a problem on projection into subspaces.

License: Creative Commons BY-NC-SA

[joeysanchez]

"In a humanely fast fashion" That's the best

[BrickBreaker]

In vector analysis, projection onto the plane is just v - (v • û), where û is the unit normal.

[lloydstagg]

At the 8'30" mark I was puzzled by the rapid way (N^t*N)^-1 became 1/3 given that it's fundamental component of Least Squares via matrices. So I checked: it's correct. Thinking about it I realised that here N is a 1-D column vector making N^t*N a dot product with a scalar result. Very neat. Another advantage of projecting onto a 1-D space compared to a higher dimension space. TFTV

[andyralph]

He is good! Very good recitation! Thank you for that alternate explanation!

[onatgirit]

3:27 1 over WHAT!! Prof. would be damned lol

[zhangkai_nodeee]

7:08 I don't understand why division on both sides is available. This is not a property that can be used in matrix calculation I think.

[vikraal]

Isn't (1, -1, 0) and (1, 0, 1) the basis for Null Space?
And not the Col Space.

[HaN-jmhe]

cant we just compute projection of b then subtract it from b to find the projection onto normal vector?

[Abhi-qiwm]

How'd he get the basis for the plane??

[castlefrank]

isn't the basis for the plane is (-1, 1, 0) and (1, 0, 1) if we put the equation into parametric form?

[rbiswas]

here you solved only projection matrix, but it is not orthogonal ?

[abdulaziz.j]

both solution are not matching !!! something is wrong

[thedailyepochs]

what reasoning did he use to get the basis columns for the plane at the beginining

[bridge]

When he calculates (N_transpose N)^-1, how is he able to directly write 1/3. Though it is correct, but how can one get an intuition to that. I thought it would be 1x1 matrix with only entry of 1/3, why am I wrong? I am wrong because if we take it as [1/3], then we wouldn't be able to multiply it with row vector [1 1 -1].

[alagappank]

How he take basis vector for A please tell me....

[rohitn]

bruh, a1 and a2 are not even independent, how can they be the basis for the plane -_-
(no hatred, the other parts of the recitation was pretty good)

[jack]

You're even using some techniques that prof. Strang haven't taught us yet. This is a bad recitation. By watching this video, we're being more confused instead of being more familiar to the lecture.