matrix choose a matrix

Рет қаралды 10,553

2 жыл бұрын

matrix choose a matrix. Calculating the number of matrix combinations of a matrix, using techniques from linear algebra like diagonalization, eigenvalues, eigenvectors. Special appearance by simultaneous diagonalizability and commuting matrices. In the end, I mention the general case using the gamma function transformation, a generalization of the factorial. Enjoy this linear algebra extravaganza.
Matrix root of matrix: • Matrixth Root of a Matrix
Matrix Factorial: • matrix factorial
Euler's Secret: • Euler's Secret
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Пікірлер: 53

@Icenri 2 жыл бұрын

Next step should be integral from 0 to matrix!

@iabervon 2 жыл бұрын

I wonder if this actually gives the x^By^(A-B) coefficient in the expansion of (x+y)^A in some sense.

@drpeyam 2 жыл бұрын

Would be interesting to figure out

@r75shell 2 жыл бұрын

This is the Peyam I like

@timothyaugustine7093 2 жыл бұрын

Why? What happened? 😐

@r75shell 2 жыл бұрын

@@timothyaugustine7093 Initially I subscribed to Payam when his videos were about some crazy stuff like half-derivative and etc. And this video fits perfectly.

@MarcusCactus 2 жыл бұрын

There are two types of Peyam videos. Those for learned curious amateurs, like this one, and those for common high-school-level learners.

@MrQwefty 2 жыл бұрын

This is getting craaaazy! Might I suggest something even crazier... The matrixth derivative!?

@WhattheHectogon 2 жыл бұрын

you've gone too far!

@MichaelRothwell1 2 жыл бұрын

I was quite flabbergasted by the idea of matrix choose matrix. Then I wondered if you would be using diagonalisation or the Gamma function... BTW, was it just a coincidence that D=A-B?

@drpeyam 2 жыл бұрын

I think it’s a coincidence :)

@reader4795 2 жыл бұрын

Great material :)

@platosbeard3476 2 жыл бұрын

Those matrices are going places!

@ahmadkalaoun3473 2 жыл бұрын

Very interesting :) Please can you share the link to the video where you prove that statement about commutative matrices?

@mimithehotdog7836 2 жыл бұрын

Now this is epic

@cameronspalding9792 Жыл бұрын

When you take the factorial of a matrix, I assume it’s well defined provided the eigenvalues are not negative intigers

@JeremyGluckStuff 2 жыл бұрын

I wonder what this could be used for.

@derwolf7810 2 жыл бұрын

There are "(n choose k)" ways to choose an (unordered) subset of k elements from a fixed set of n element. I wonder, is there something similar for matrices... so some kind of realationship of sth for which that matrix is a value for?

@noahtaul 2 жыл бұрын

In B, should the top-left entry be 6?

@joefarrow1599 2 жыл бұрын

Did you define this operation yourself? Or is it used in the literature?

@theproofessayist8441 2 жыл бұрын

Wonder what taking a selection of a permutation would be like? hmmmm!

@cameronspalding9792 Жыл бұрын

@ 4:10 I believe you made a bracketing error

@BrutishLearner4 2 жыл бұрын

Awesome video! :) Really interesting. Is there any applications of this somewhere? For example, is it part of some well-known proofs of various theorems, maybe it’s used somewhere in applied maths or physics? Also is there any intuition one can apply to this in a similar way as the usual n choose m? Also keen to see more stuff like this, it’s really interesting

@drpeyam 2 жыл бұрын

Quantum mechanics probably hahaha

@tanmaymishra9576 Жыл бұрын

only for AB=BA matrices

@pussy2907 2 жыл бұрын

Can you explain function of matrix which is not diagonalisable with good example

@drpeyam 2 жыл бұрын

Already done

@MarcusCactus 2 жыл бұрын

Does the order of < B!(A-B)! > have anything to do with the order of < A! (blabla!)^-1 > ?

@mathaddict9973 2 жыл бұрын

This is crazier than the i’th derivative, (i=sqrt(-1)) lol, love it

@MrRyanroberson1 2 жыл бұрын

so, you've done matrix^matrix, what about tetration? 3^^3 = 3^27, and all. exponentiation of matrices i can understand is an extension of the exponential, which is definable via polynomials, however for tetration i think it is generally impossible to have a matrix anywhere other than the base; still it would be cool to see what M^^4 is, for some matrix M, you would probably want to use B (from this video) since tetration explodes really fast for bases larger than 2

@drpeyam 2 жыл бұрын

Very interesting, thank you!

@user-dq5fz5ph6e 2 жыл бұрын

First time i see this thing ....

@goblin5003 2 жыл бұрын

Agreed, this is such an original idea

@halglick Жыл бұрын

I got complex eigenvalues for B. did I mess up somewhere?

@drpeyam Жыл бұрын

Possibly

@halglick Жыл бұрын

@@drpeyam huge fan :D. By the way, I played around with B and found out that it works when you use 4 instead of -4, but I am probably being nit-pickey.

@dougr.2398 2 жыл бұрын

Your matrix of matrices?

@kiit8337 2 жыл бұрын

Miss ur bunny 🐰.. 😙🥺🥺

@drpeyam 2 жыл бұрын

Same 🥺🥺

@MrRyanroberson1 2 жыл бұрын

actually this makes me wonder since out of all values for 1/gamma(x), the only zeroes are at negative integers, doesn't this mean you can define things like... 2 choose 8.5, and it won't be zero, even though it is total nonsense (in terms of its origin)? i don't know why this is something i only noticed during THIS video

@drpeyam 2 жыл бұрын

Of course you can define 2 choose 8.5