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 Apr 23 awarded Nice Question Apr 11 awarded Nice Question Apr 10 awarded Popular Question Mar 30 awarded Nice Question Mar 30 awarded Popular Question Mar 15 awarded Notable Question Feb 6 awarded Cleanup Feb 6 revised Prove that $\vdash p \lor \lnot p$ is true using natural deduction rolled back to a previous revision Dec 3 comment Friend B and C have eaten zero apples. How many more apples has C eaten? haha good point @user46944 Dec 3 asked Friend B and C have eaten zero apples. How many more apples has C eaten? Nov 30 awarded Yearling Nov 27 awarded Famous Question Nov 24 answered Spectral theorem for matrices Nov 21 comment Given $A$ a symmetric square matrix. Why is $f_A: O(n) \to \mathbb{R}^{n \times n}: Q \mapsto Q^{\top} A Q$ continuous? In what kind of book could I learn about why matrix multiplication, $Q\mapsto Q^{-1}$ is continuous, and $Q\mapsto Q^\top$ is continuous? I own Topology by James R. Munkres, would that be a good one? @GEdgar Nov 21 comment Given $A$ a symmetric square matrix. Why is $f_A: O(n) \to \mathbb{R}^{n \times n}: Q \mapsto Q^{\top} A Q$ continuous? @mathcounterexamples.net First things that come to mind is that $f^{-1}(A)$ is open for every open subset $A$ of $O(n)$. Nov 21 comment Given $A$ a symmetric square matrix. Why is $f_A: O(n) \to \mathbb{R}^{n \times n}: Q \mapsto Q^{\top} A Q$ continuous? Then every entry is a polynomial of $q_{11}, ... , q_{nn}$ and therefore continuous. Nov 21 comment Given $A$ a symmetric square matrix. Why is $f_A: O(n) \to \mathbb{R}^{n \times n}: Q \mapsto Q^{\top} A Q$ continuous? @GEdgar It is some time ago, since I studied this. But something things are coming back. Could/should I see it as a mapping $f_A: \Bbb R^{n\times n} \to \Bbb R^{n\times n}$ because then it makes more sense to me. With the euclidean metric. Nov 21 comment Given $A$ a symmetric square matrix. Why is $f_A: O(n) \to \mathbb{R}^{n \times n}: Q \mapsto Q^{\top} A Q$ continuous? @GEdgar I have surely proved that a couple of years ago in a real analysis course. But with matrices, I get a bit confused to be honest. Nov 21 asked Given $A$ a symmetric square matrix. Why is $f_A: O(n) \to \mathbb{R}^{n \times n}: Q \mapsto Q^{\top} A Q$ continuous? Oct 20 awarded Notable Question