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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 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
Prove that the manifold $SO(n)$ is connected The question really is that simple: Prove that the manifold SO(n) ⊂ GL(n,R) S O (n) ⊂ G L (n, R) is connected it is very easy to see that the elements of SO(n) S O (n) are in one-to-one correspondence with the set of orthonormal basis of Rn R n (the set of rows of the matrix of an element of SO(n) S O (n) is such a basis) My idea was to show that given any orthonormal basis (ai)n1 (a i
How to find the difference between the sons and mothers age if it . . . 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 and finds out that this whole 'age' reversed process occurs 6 times And if they (mom + son) were lucky it would happen again in future for two more times
Lie Algebra of U(N) and SO(N) - Mathematics Stack Exchange U(N) and SO(N) are quite important groups in physics I thought I would find this with an easy google search Apparently NOT! What is the Lie algebra and Lie bracket of the two groups?
modular form -Petersson inner product - Mathematics Stack Exchange my question is about Petersson inner product i need to prove that $ (E_k,f) =0 $ $\forall f \in S_k (SL_2 (\mathbb {Z}))$ the only thing that i think that should help me is that the space of cusp fo
Improper integral of sin(x) x from zero to infinity I was having trouble with the following integral: ∫∞ 0 sin(x) x dx ∫ 0 ∞ sin (x) x d x My question is, how does one go about evaluating this, since its existence seems fairly intuitive, while its solution, at least to me, does not seem particularly obvious
In a family with two children, what are the chances, if one of the . . . For example, suppose there is a social science study on 2 child families with at least 1 daughter-- in this situation, about 1 3 of the families will be daughter-daughter, 1 3 will be daughter-son, and 1 3 will be son-daughter You have to consider the full probability space of two trials (d-d,d-s,s-d,s-s) and eliminate the s-s possibility