Suppose $H_1, H_2$ are $n \times n$ Hermitian matrices and $A(\lambda) = H_1 + \lambda H_2$ is a $\lambda$ matrix. I need to show all $A(\lambda)$'s invariant factors are real polynomials. I attempted to prove this by induction on $n$. It works well except for the case that all diagonal elements ...
How to arrange following irrational numbers in ascending order: $$ 2^{\sqrt{\frac{5}{3}}}, 3^{\sqrt{\frac{3}{5}}}, 5^{\sqrt{\frac{4}{15}}}, 29^{\frac{1}{\sqrt{15}}} $$ My try: Using a calculator I computed the values $$ 2^{\sqrt{\frac{5}{3}}}\approx 2.445, \quad 3^{\sqrt{\frac{3}{5}}}\approx 2.34...
Proposal: Remove gre-exam, gmat-exam. These are meta tags with very bare-bones tag wikis. Furthermore, there aren’t any other tags for important math exams, i.e. the IMO or USAMO, so why should we make an exception for these two?
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