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WHY DO $SO(N,\\MATHBB{R})$ AND $O(N,\\MATHBB{R})$ HAVE THE …
Jan 22, 2022 If one is willing to avoid all of the details regarding special types of matrices, there is a simple abstract reason that O(n;R) O (n; R) and SO(n;R) S O (n; R) should have the same …
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IS $SO(N)$ ACTUALLLY THE SAME AS $O(N)$? - MATHEMATICS STACK …
May 23, 2016 In the current problem, X X is a member of so(n) s o (n) (or of o(n) o (n)). Now since all members of o(n) o (n) are anti-symmetric matrices which have all its diagonal …
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THE TUESDAY BIRTHDAY PROBLEM - MATHEMATICS STACK EXCHANGE
In case this is the correct solution: Why does the probability change when the father specifies the birthday of a son? (does it actually change? A lot of answers/posts stated that the statement …
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LIE GROUPS - LIE ALGEBRA OF SO (N) - MATHEMATICS STACK EXCHANGE
Apr 24, 2017 Where a, b, c, d ∈ 1, …, n a, b, c, d ∈ 1, …, n. And so(n) s o (n) is the Lie algebra of SO (n). I'm unsure if it suffices to show that the generators of the ...
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CONTRAST BETWEEN SO (N) AND SPIN (N) REPRESENTATION
Jul 20, 2020 Earlier I asked this Comparison between SO(n) and Spin(n) representation theory which is closed. I think the question is certainly valid and a good one. But my comments are …
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HOW TO FIND THE DIFFERENCE BETWEEN THE SON'S AND MOTHER'S AGE IF IT ...
Oct 23, 2019 A son had recently visited his mom and found out that the two digits that form his age (eg :24) when reversed form his mother's age (eg: 42). Later he goes back to his place …
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WHAT IS THE RELATIONSHIP BETWEEN SL (N) AND SO (N)?
To add some intuition to this, for vectors in Rn R n, SL(n) S L (n) is the space of all the transformations with determinant 1 1, or in other words, all transformations that keep the …
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DIMENSION OF SO (N) AND ITS GENERATORS - MATHEMATICS STACK …
Nov 18, 2015 The generators of SO(n) S O (n) are pure imaginary antisymmetric n × n n × n matrices. How can this fact be used to show that the dimension of SO(n) S O (n) is n(n−1) 2 n …
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FUNDAMENTAL GROUP OF THE SPECIAL ORTHOGONAL GROUP SO(N)
Question: What is the fundamental group of the special orthogonal group SO(n), n> 2? Clarification: The answer usually given is: Z2. But I would like to see a proof of that and an …
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PROBLEM SOLVING - DIOPHANTUS' LIFESPAN - MATHEMATICS STACK …
"The son lived exactly half as long as his father" is I think unambiguous. Almost nothing is known about Diophantus' life, and there is scholarly dispute about the approximate period in which he …
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