query: Showing that Lie($U(n)$)=$\mathfrak{u}(n)$
positive_passages.docid: 114626
positive_passages.text: Lie Algebra of U(N) and SO(N)
negative_passages.docid: 147399
negative_passages.text: Proof of "$L$ / Rad$L$ is semisimple for arbitrary Lie algebra L".
negative_passages.docid: 98660
negative_passages.text: (complex measures) $d\nu=d\lambda +f\,dm \Rightarrow d|\nu|=d|\lambda| +|f|\,dm$ and $f\in L^1(\nu)\Rightarrow f\in L^1(|\nu|)$
negative_passages.docid: 34147
negative_passages.text: $\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
negative_passages.docid: 14576
negative_passages.text: $(U\cap W)^0 = U^0 + W^0$
negative_passages.docid: 124882
negative_passages.text: Killing form on $\mathfrak{sp}(2n)$
negative_passages.docid: 111814
negative_passages.text: Precise connection between complexification of $\mathfrak{su}(2)$, $\mathfrak{so}(1,3)$ and $\mathfrak{sl}(2, \mathbb{C})$
negative_passages.docid: 121880
negative_passages.text: How to show that $|D_{2n}| = 2n$ via the presentation?
negative_passages.docid: 68385
negative_passages.text: Prove that $ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} $
negative_passages.docid: 24585
negative_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
negative_passages.docid: 77891
negative_passages.text: $(U\circ T)^{*} = T^{*}\circ U^{*}$
negative_passages.docid: 157742
negative_passages.text: Prove that $U(n)$ is a manifold
negative_passages.docid: 51889
negative_passages.text: How to "find" this Lie algebra: proof that $\mathfrak{sl}$ is trace zero matrices
negative_passages.docid: 23535
negative_passages.text: Describing the Lie algebra structure of a semi-direct product of Lie groups
negative_passages.docid: 76694
negative_passages.text: Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
negative_passages.docid: 145509
negative_passages.text: Prove the roots of $p(z)+z^n\bar{p}(\frac{1}{z})$ lie on the unit circle
negative_passages.docid: 133884
negative_passages.text: A proof using Yoneda lemma