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 Sep 15 comment Can all real numbers be represented by the sum of a convergent series? Your sum is trivial since if we let $x=2$, we get $\sum_{n=0}^\infty\frac{1}{2^n}=2$. Hence you can choose $k$ and $m$ such that $\frac{k}{m}\cdot 2=\ell$, where $\ell\in\mathbb{Q}$ is any rational you like. Sep 14 comment Find all complex numbers $z$ satisfying the equation- $|z + 1| = |\bar{z} − 1|.$ General tip: When presented with a problem like this, think about what you know. A few "facts" that spring to my mind immediately are: $|w|^2=w\bar{w}$, and for $w=x+iy$ then $\bar{w}=x-iy$. See also Daniel Fischer's comment. Apply what you know and see what follows logically. Hopefully it will be the answer! Sep 10 comment Turning 500, 1100, 1800, 2600, 3500, etc into 1, 2, 3, 4, 5, etc We have $f (n) = 50 n(9 + n)$, so just use the quadratic formula to get $n$. Sep 7 accepted Does $A,B\in M_{n\times n}$ both lower triangular imply simultaneous triangularization? Sep 6 asked Does $A,B\in M_{n\times n}$ both lower triangular imply simultaneous triangularization? Aug 27 comment Evaluating This Complex Line integral Yes. But as you say it's rather ugly ! See Jack's answer below... Aug 27 comment Evaluating This Complex Line integral You could try letting $z=\sin(t^2)-i\frac{2t^2}{\pi}$ and substitute into the integral. Use the limits $0$ and $\sqrt{\pi/2}$. But maybe you tried that already. Aug 26 comment Abuse of notation ? $(A\mid M_{n\times p})$ to denote a set of matrices… @A.G. Good point ! Aug 26 revised Abuse of notation ? $(A\mid M_{n\times p})$ to denote a set of matrices… edited title Aug 26 comment Abuse of notation ? $(A\mid M_{n\times p})$ to denote a set of matrices… A matrix in $M_{n\times (m+q)}$ where $q$ is the number of columns of $B$, so long as $B$ has $n$ rows. At least that's what I'd want it to be... Aug 26 revised Abuse of notation ? $(A\mid M_{n\times p})$ to denote a set of matrices… added 6 characters in body Aug 26 comment Abuse of notation ? $(A\mid M_{n\times p})$ to denote a set of matrices… Ah yes i see as they're both sets of matrices. Aug 26 revised Abuse of notation ? $(A\mid M_{n\times p})$ to denote a set of matrices… deleted 39 characters in body Aug 26 asked Abuse of notation ? $(A\mid M_{n\times p})$ to denote a set of matrices… Aug 26 revised Is this “truncating” matrix function well known? deleted 3 characters in body Aug 26 comment Is this “truncating” matrix function well known? Ok, thanks all. I think I'll stick with my $\tau$ definition. As A.G. says, submatrix is good, but my submatrix is very special so the usual notation may be overkill. I don't think $A_r$ would be great because my matrices can be made up many multiplications, so it may be confusing. I like the idea of projection, but projections have a huge theory surrounding them and I don't intend to use that where $\tau$ is concerned. I may be using projections later on, so this might also cause confusion if mixing notation. Interesting to be reminded of submatrices and projections in this context though ! Aug 26 comment Is this “truncating” matrix function well known? Maybe my original definition in the question is fine then? Aug 26 comment Is this “truncating” matrix function well known? Good point ! Thanks. I think using $\pi_r$ would be more natural. Aug 26 comment Is this “truncating” matrix function well known? So maybe I could say "... define the projection $\pi_r:M_{n\times n}\to M_{n\times r}$ where $r\leq n$..." without having to mention how the function is defined due to the presence of the word "projection" in the definition statement. Aug 26 asked Is this “truncating” matrix function well known?