@@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?
@@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.
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
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.
Next step should be integral from 0 to matrix!
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
This is getting craaaazy!
Might I suggest something even crazier... The matrixth derivative!?
you've gone too far!
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!
Great material :)
@ 4:10 I believe you made a bracketing error
Did you define this operation yourself? Or is it used in the literature?
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?
When you take the factorial of a matrix, I assume it’s well defined provided the eigenvalues are not negative intigers
only for AB=BA matrices
Wonder what taking a selection of a permutation would be like? hmmmm!
Now this is epic
I wonder what this could be used for.
In B, should the top-left entry be 6?
Neat. But is it applicable to any real world problems?
Quantum mechanics
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.
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!
Does the order of < B!(A-B)! > have anything to do with the order of < A! (blabla!)^-1 > ?
“…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
First time i see this thing ....
Agreed, this is such an original idea
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 😊
Your matrix of matrices?
This is crazier than the i’th derivative, (i=sqrt(-1)) lol, love it
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
Don't you need to worry about the degeneracy of the matrices to apply this trick?
Miss ur bunny 🐰.. 😙🥺🥺
Same 🥺🥺
矩陣真是煩人，暈了。
Understood nothing.