Proof verification: Prove that a tree with n vertices has n-1 edges What you are fundamentally saying is that if you have a tree with n vertex and n-1 edges, you can obtain a tree with n+1 vertices and n edges You can add the new edge to any of the previous vertex, but how you didn't prove that doing this way you'll exhaust all the trees with n+1 vertices
linear algebra - Showing that $l_2$ norm is smaller than $l_1 . . . Yes And thanks for reaching out and asking It is the Minkowshi inequality under repeated use, where the measure employed is the counting measure Here is the idea: The M inequality says that ∥f + g∥ ≤ ∥f∥ + ∥g∥ ‖ f + g ‖ ≤ ‖ f ‖ + ‖ g ‖ $\Vert f+g\Vert \le \Vert f\Vert +\Vert g\Vert$ So if we apply it multiple times we can see that ∥f + g + h∥ ≤ ∥f + g∥
Product of inverse matrices $ (AB)^{-1}$ I am unsure how to go about doing this inverse product problem: The question says to find the value of each matrix expression where A and B are the invertible 3 x 3
Normalize values to sum 1 but keeping their weights 40 10 I need to format these numbers so that they form the sum 1, but they should keep their "weight" In this specific case: 40 would become 0 80 10 would become 0 2 But if I have more values (like 40, 10, 25, 5 for example), I am really lost because I don't know the formula