เนื้อหาของบทความนี้จะพูดถึงarctan 30 หากคุณกำลังมองหาเกี่ยวกับarctan 30มาถอดรหัสหัวข้อarctan 30กับpopasia.netในโพสต์Arctan of a Matrixนี้.
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ภาพรวมที่ถูกต้องที่สุดของเนื้อหาที่เกี่ยวข้องเกี่ยวกับarctan 30ในArctan of a Matrix
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#Arctan #Matrix.
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Arctan of a Matrix.
arctan 30.
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Sir ,is it applicable for every diagonalizable square matrix? As we are using Taylor series sum which converges when |x|<1 ,so which matrix will be converges?
I felt like I was unique by coming up with this idea. I had a slightly different approach (yours is probably better), but same concept. It's useful when computing square roots or inverse roots or any sort of rotation between column vectors.
I'd do stuff like take a gram matrix of a few column vectors because reducing the problem to a 2×2 matrix is something I know how to deal with.
Eigenvectors is still something I have trouble wrapping my mind around. It's wild how there's an infinite number of ways to orthonormalize a matrix and how they're all basically the same thing rotated different ways even though the vectors don't necessarily resemble each other.
He knew that doing the same thing for a 3*3 matrix is going to be way longer ///
Simple , clear and new wow!!! DrRahul Rohtak Haryana India
How can we do it in Matlab?
Please, pppleeeease, pretty please, goddamn please!
Don't use the '-1' exponent to express reciprocals.
What does "tan^-2" mean then ? Is it "1/tan^2" or the square of arctan?
See? There exists the term ARCtan, ARCsin, ARCcos!
Thank you.
What the result of the video means is that tan of the final matrix is A. Direct proof:
As Ishay Weissman noted, A^k=A for any positive integer power k. Let B = arctan A which we saw = π/4 A. So B^k = (π/4)^k A. So if p(x) is any polynomial in x with no constant term we get p(B) = p(π/4) A. Taking limits, the same is true for any power series function p(x) with no constant term. In particular, tan B = tan π/4 A = 1A = A. QED
5:00 P Diddy! 😀
New to the channel, great informational content and zeal!
You can go back and Apply the tan to the result (it has exactly the same P and P^-1) matrix and u got the original one ✔ i have already done this and it fits perfect , amazing video
I feel like you're putting mathematical physics on blast at the end there. If you want to take it to the next level start mentioning [some weird word like informal] fields theory, or (possibly anti) de sitter space correspondence, mirror bisymmetry.
Wuuu dos equis !! I love when you mix español
This reminds me of interpreting zippers as analytical derivation of original data structure.
Derivation of list data structure, derivation of tree data structure.
But dr.peyam…this is crazy
Dr.peyam : yeahh…crazy awesome!
Love you sir 😀
Can you find the logarithm with a matrix base to a matrix?
Sir can you do a video on matrix differentiation. Please.
Actually, the most part of quantum mechanics is based on the Spectral Theorem of a selfadjoint operator which is a generalization of the diagonalization in linear algebra. That proves he is a true math guy <3
What restrictions to matrices are there, if the radius of convergence of our series expansion is not the real numbers. For example, for what nxn-matrix A does arcsin(A) or ln(A) have a proper solution?
Dos equis lmaoooo
Uhm… I'll try to do the same with Binet formula…
Is it A – (lamda x I) or (lamda x I) – A ? Because you change the sign of the matrix
A^2 = A so we can simply write (by factorisation on the Taylor series of arctan) : arctan(A) = A arctan(1) = A.pi/4
I'm a theoretical physicist and I believe it's possible to use this result when you're integrating a specific combination of momentum operators. So, indeed. There is a quantum mechanical interpretation. = )
Nice to see. I have used the same trick in my theses. For interpretation of my experimatal data it contained some quantum mechanical calcualtion of electron transistions in 2 dimensional semiconducter structures in high magnetic field disturbed by charged donors. The donor potential was some 1/r function, which had to be evaluated in the plane of the electrons.
I cant understand the result because tan-1(2) is not pi/2
This is a trivial example, no need to diagonalize. Here A^k=A for all k=1,2, … so, one can put A in front of the Taylor expansion of arctan(1) and get ( pi/4)A.
I guess you can evaluate most functions f(A) with A as a matrix by just diagonalising A, then having f(A) = P f(D) P^-1. My attempt at making sense of this is that f can be expressed as a sum of (an infinite number of) powers of A, and we already know how to raise a matrix to an integer power! So this way, we continue as normal, then once we are done, just find P and D, then evaluating f(D), which is much easier since we know how to raise a diagonal matrix to a power easily! Therefore, we can just apply the infinite series to D, which will give us the answer!
(My explanation isn’t very good, but it’s all I got)
We could factorise the π/4 from the arctan(D) then we get the original D and later only (π/4)A.
Thank you for the content!
What does this mean? I have no idea… Haha
Ur hair have grown, u look handsome
Thank you for this video. But main problem can be appear as eigenvalues are the same, then matrix can be sometimes with "ones" over the main diagonal of a matrix, and also use functions for them. The main question for me now is about finding eigenvectors of this matrix, where it's values are repeating, and, also, situations where they can be linearly independent. The main usage of this type functions is solving systems of ODE's, which video you also has on a channel, but there also didn't mentioned when roots can be repeating, and lines can be independent for repeating roots. I hope you'll make more videos about linear algebra, and matrix transformations.
I tried it with Pauli X and Pauli Z matrices, turned out arctan A is π/4 A, just as in this video
Wow the tan^-1 of this matrix is a scalar multiple (π/4) of the matrix.
Thanks Dr peyam, amazing as always!
Wow. Iconic Dr. Peyam like always!!!
Incredible
I don't believe in this
“X, y equals dos eckies” 😉
Really good job Prof. Peyam
great video and lesson!! Thank you!!!
I hope you're doing well in this crisis, Dr. Peyam…
(Tired of online lectures I'm sure)
Which major did you choose ? And where did you study? Thank you!
Diagonalizable matrices are so useful! Great video!
When you get bored in Linear Algebra because your class goes so slowly, and you pull out your 30th piece of scratch paper…
Why
The radius of convergence would be the same as arctan, [-1,1], for the eigenvalues. Can you take the arctan of a matrix that you can't diagonalize? If so it wouldn't be easily computed bc taking higher powers of a matrix that's non-diagonalizable is generally hard (some exceptions like rotation matrices)