@@timothyaugustine7093 Initially I subscribed to Payam when his videos were about some crazy stuff like half-derivative and etc. And this video fits perfectly.
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?
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
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?
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 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.
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
This is the Peyam I like
Why? What happened? 😐
@@timothyaugustine7093 Initially I subscribed to Payam when his videos were about some crazy stuff like half-derivative and etc. And this video fits perfectly.
There are two types of Peyam videos. Those for learned curious amateurs, like this one, and those for common high-school-level learners.
This is getting craaaazy!
Might I suggest something even crazier... The matrixth derivative!?
you've gone too far!
I wonder if this actually gives the x^By^(A-B) coefficient in the expansion of (x+y)^A in some sense.
Would be interesting to figure out
Next step should be integral from 0 to matrix!
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?
I think it’s a coincidence :)
Very interesting :)
Please can you share the link to the video where you prove that statement about commutative matrices?
Those matrices are going places!
Did you define this operation yourself? Or is it used in the literature?
Great material :)
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
Quantum mechanics probably hahaha
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?
Does the order of < B!(A-B)! > have anything to do with the order of < A! (blabla!)^-1 > ?
When you take the factorial of a matrix, I assume it’s well defined provided the eigenvalues are not negative intigers
Now this is epic
@ 4:10 I believe you made a bracketing error
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
Very interesting, thank you!
In B, should the top-left entry be 6?
I got complex eigenvalues for B. did I mess up somewhere?
Possibly
@@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.
only for AB=BA matrices
Isn't (0)Choose(0) = 1? Shouldn't the results of (D)Choose(E) be written as: [15 1; 1 6], instead of [15 0: 0 6]?
You only do the choosing on the diagonal entries, the non diagonal ones are 0 :)
@@drpeyam okay, thanks 😊
Wonder what taking a selection of a permutation would be like? hmmmm!
This is crazier than the i’th derivative, (i=sqrt(-1)) lol, love it
I wonder what this could be used for.
First time i see this thing ....
Agreed, this is such an original idea
Neat. But is it applicable to any real world problems?
Quantum mechanics
“…for diagonal matrices, D choose E, that’s just the choosing part on the eigen values”. how do we know this?
Because D^n is just the eigenvalues to the n th power
@@drpeyam sorry, what? I knew that, but how does that relate to this?
Well a factorial is a gamma function which is a power series, which is a sum of D^n
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
Of course you can define 2 choose 8.5
Miss ur bunny 🐰.. 😙🥺🥺
Same 🥺🥺
Your matrix of matrices?
Don't you need to worry about the degeneracy of the matrices to apply this trick?
Understood nothing.
矩陣真是煩人，暈了。