Ytukyg

up vote 2 down vote favorite This question already has an answer here: Standard argument for making the class group of a number field trivial 1 answer Let $F$ be a number field, and $mathcal{O}$ its ring of integers. Is there always a finite set $S$ of places of $F$ such that $mathcal{O}_S$ has class number one? Is it a consequence of standard results on class field theory or is it something else? number-theory algebraic-number-theory class-field-theory share | cite | improve this question asked Nov 26 at 7:06 TheStudent

up vote 10 down vote favorite Cauchy-Schwarz inequality applied to Trace of two products $mathbf{Tr}(A'B)$ has the form $$ mathbf{Tr}(A'B) leq sqrt{mathbf{Tr}(A'A)} sqrt{mathbf{Tr}(B'B)} $$ I saw many places where people use this inequality. But did not see a formal proof. Is it difficult to prove ? Anyone can give a simple proof ? linear-algebra trace cauchy-schwarz-inequality share | cite | improve this question asked Nov 20 at 9:23 Shew 553 4 13 closed as o