- Boy Born on a Tuesday - is it just a language trick?
The only way to get the 13 27 answer is to make the unjustified unreasonable assumption that Dave is boy-centric Tuesday-centric: if he has two sons born on Tue and Sun he will mention Tue; if he has a son daughter both born on Tue he will mention the son, etc
- Book recommendations for linear algebra - Mathematics Stack Exchange
I have been wanting to learn about linear algebra (specifically about vector spaces) for a long time, but I am not sure what book to buy, any suggestions?
- Fundamental group of the special orthogonal group SO(n)
Question: What is the fundamental group of the special orthogonal group SO(n) S O (n), n> 2 n> 2? Clarification: The answer usually given is: Z2 Z 2 But I would like to see a proof of that and an isomorphism π1(SO(n),En) → Z2 π 1 (S O (n), E n) → Z 2 that is as explicit as possible I require a neat criterion to check, if a path in SO(n) S O (n) is null-homotopic or not Idea 1: Maybe
- Dimension of SO (n) and its generators - Mathematics Stack Exchange
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 (n 1) 2? I know that an antisymmetric matrix has n(n−1) 2 n (n 1) 2 degrees of freedom, but I can't take this idea any further in the demonstration of the proof Thoughts?
- 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 volume constant This is because the determinant is what one multiplies within the integral to get the volume in the transformed space SO(n) S O (n) is the subset in which the transformation is orthogonal (RTR
- lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange
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
- Contrast between SO (n) and Spin (n) representation
In contrast, the Spin (3) group has a trivial representation, and other odd and even-rank dimensional matrix representation:
- semi-simple and simple lie group,SO (n) for n even
You should edit your question using MathJax More importantly, you should use SO(n) S O (n) instead of so(n) s o (n) (the latter would be the notation for a Lie algebra) Lastly, do you know the definition of a simple (semisimple) Lie group?
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