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 Apr17 comment Showing existence of a spanning tree in a graph with two kinds of edges using $k$ of one kind of edge I think you need a slight tweak here. If you order your edges such that when you add your first edge, it creates a cycle of all blue edges, you end up with an $A'$ that still has $\ell$ blue edges. However, I believe that you can always choose your edge to add such that it does not create an all blue cycle (assuming $\ell\neq m$), because if you can't, then you already have a spanning tree with the maximum number of blue edges, namely $m$ of them. Convoluted, but I think this covers it. Apr17 comment Calculation of a 'double' sum How are you interpreting your bounds on the sums when $\frac{n}{2}$ and $\sqrt{n}$ are not whole numbers? Nov1 comment Example of a vector norm for which $\|I\|<1$ @Gortaur I saw your answer, thank you for the effort! Nov1 comment Example of a vector norm for which $\|I\|<1$ @OlivierBégassat Well I feel only slightly more silly for not seeing this prior, thanks for the hint. Nov1 comment Equivalence of a Vector Norm being Absolute That makes sense. The explanation is/was clear, I was just worried about the assumptions made to derive it. Thanks. Nov1 comment Equivalence of a Vector Norm being Absolute Doesn't this violate the hypothesis that this must hold for all $\alpha_i$? I read "...for all $x$ and all $y$..." to mean any combination of arbitrary $x$ and $y$