These are orthogonal #shorts

A better attempt at the format. #shorts

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[Juan_Carls]

A very similar approach: I noticed that (Av)*v=(Av)^T v = v^T A^T v = -v^T (Av) = - [(Av)^T v]^T = - (Av)^T v (the last equality is true bc the matrix/dot product is a scalar). Then (Av)*v = 1/2[(Av)^T v - (Av)^T v] = 0.
And that's a good place to stop

[tinnguyen]

Looking forward to Linear Algebra stream in January!!

[chenardpierre]

Should we add the assumption that the characteristic of the field is different from 2?

[francoborgarello]

Something that I find interesting is that skew-symmetric matrices (A^T = -A) are a vector space with dim 3 (of course, assuming that A is 3x3). So, in R3, you can "associate" every vector with one of these matrices. And, if you multiply one matrix A associated with a vector v, with another vector w, A times w is equal to the cross product between v and w.

[elevedesfb]

<Av, v> = <v, A(dual)v> = <v, A(transpose)> = <v, -Av> = -<v, Av> = -<Av, v>

Hence 2<Av, v> = 0 and this is a good place to stop

[fedorlozben]

(Av)t*v=vtAt*v=-vt*Av
The last can be rewritten as at*b=bt*a because it is a summ of components multiplied in any way...but then first and last(without negative sign) are equal.
(Av)t*v=-vt*Av
(Av)t*v=vt*Av
Then it is zero in any way.
I wish this way is more easier for understanding what happens with this class of matrixes

[trogdorX]

TFW you try to speedrun a math problem (any% WR)

[dfnstrt]

Orthogonal shorts sound a bit like Pythagoras's Pants (a common description of the diagram illustrating the Pythagorean Theorem in Russian)

[albertogarcia]

The usual inner product on F^n, F being a field with characterist 0, is defined by x.y:=(x^t)y, with the right side the matrix product of the row vector x^t times the column vector y, is communtative. I dont see why v.Av=(A^tv).v, should be on place v.Av=(Av).v, the trick is not clear yet

[alirezaghadami]

These are called skew symmetric matrices...

[orangeguy]

Why not use definition of dot product v.w = v^Tw (row times column)

[franolich]

I really don't understand the current fad for fast maths videos. If there is something interesting and/or challenging to present, rushing through it just makes it harder to appreciate. Otherwise the speed is just a distraction from the fact that there is no interesting content and frankly is merely an attempt to show off.

I would much rather have a slower paced, normal length video with a compilation of genuinely interesting "shorts" like this one. Michael, please don't give in to current naff trends - you're too good for that!

[giorgostarnaras]

The next short plays and so its not a good place to stop😜

[alainrogez]

I don't understand how the v.A became At.v

[BizVlogs]

Liberals explaining how affirmative action isn’t racist be like: