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Apr
7
awarded  Yearling
Mar
31
awarded  Guru
Feb
17
awarded  Guru
Feb
11
comment derivatives with matrices
Are you taking the derivative evaluated at $t=0$?
Feb
7
awarded  Nice Question
Jan
30
awarded  Enlightened
Jan
29
awarded  Nice Answer
Jan
24
accepted Automorphism group of a lattice's Voronoi cell
Jan
23
comment Automorphism group of a lattice's Voronoi cell
Thank you for the proof. There are a few things I would formalize a bit, but the overall direction seems great. In particular your proof is just the fact that the facet vectors of a lattice generate it, something which I should've thought of :).
Jan
21
awarded  Nice Question
Jan
19
answered Is a permutation of block diagonals similar?
Jan
19
comment Is a permutation of block diagonals similar?
Your proof and your result are both correct. Explicitly, the two are similar through the corresponding permutation matrix, which is seen as the change of basis matrix from your original basis to your permuted one.
Jan
19
revised Automorphism group of a lattice's Voronoi cell
added 2 characters in body
Jan
18
comment Can someone direct me to prove the following three claims about a rotation group $SO(3)$ and its Lie Algebra?
@IllegalImmigrant I've added a bit on the isomorphism between the two Lie algebras.
Jan
18
revised Can someone direct me to prove the following three claims about a rotation group $SO(3)$ and its Lie Algebra?
expand on answer
Jan
18
comment Can someone direct me to prove the following three claims about a rotation group $SO(3)$ and its Lie Algebra?
Indeed this is the idea of the Lie algebra/Lie group correspondence. Many results are simpler to describe using the Lie algebra and can then be lifted to the Lie group. For $SO(3)$, it is simpler to keep track of skew-symmetric matrices (3 numbers) than it is an orthogonal matrix. There are many uses for this result in general. For example, the description of angular momenta and spin in quantum mechanics involves the representation theory of $SO(3)$, which is simplest to describe using the Lie algebra. I'll add a bit on the correspondence between the cross product and commutator in the answer.
Jan
18
comment If $A^3=A+I$, then $\det A>0$
@TienKhaPham This is the conjugate root theorem. The proof is simple and given in the link.
Jan
18
revised Can someone direct me to prove the following three claims about a rotation group $SO(3)$ and its Lie Algebra?
added 42 characters in body
Jan
18
answered Can someone direct me to prove the following three claims about a rotation group $SO(3)$ and its Lie Algebra?
Jan
18
revised Automorphism group of a lattice's Voronoi cell
error in definition