# csss

UK

Final year student in applied mathematics.

 2018 Aug 30 awarded Popular Question Aug 29 awarded Yearling Aug 26 asked When to use and $L^2(\partial \Omega)$ norm and when to use a Sobolev norm $H^{\pm 1/2}(\partial \Omega)$? Aug 16 comment Why are the round-off errors when solving the linear system $Ax = b$ of order $\varepsilon_\text{mach} x_j$?Very nice answer thanks! Can you recommend and books or papers that cover this type of material, i.e., implications of machine precision on solving $Ax=b$ type systems? Aug 16 awarded Scholar Aug 16 awarded Supporter Aug 16 accepted Why are the round-off errors when solving the linear system $Ax = b$ of order $\varepsilon_\text{mach} x_j$? Aug 13 awarded Student Aug 13 awarded Editor Aug 13 revised Why are the round-off errors when solving the linear system $Ax = b$ of order $\varepsilon_\text{mach} x_j$?added 361 characters in body Aug 13 asked Why are the round-off errors when solving the linear system $Ax = b$ of order $\varepsilon_\text{mach} x_j$? Aug 13 awarded Autobiographer Aug 8 awarded Nice Question Jan 31 awarded Popular Question Nov 17 awarded Yearling Nov 17 awarded Yearling Nov 13 awarded Famous Question Nov 7 awarded Popular Question Oct 30 comment Every invertible matrix can be written as a finite composition of elementary matrices with real eigenvalues?But invertible matrices correspond directly to automorphism, do they not? - proofwiki.org/wiki/… - how can the statement be correct for automorphisms of $\mathbb{R}^n$ but not for invertible $n\times n$ matrices if these are equivalent? Oct 30 comment $F(y) = F(x)$ for aribtrary continuous linear functional $F$, then by Hahn-Banach $y=x$?You say we assumed that $x \neq y$. I don't see how arriving at $F(x) \neq F(y)$ contradicts that original assumption?