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∥
Easy way to remember Taylor Series for log (1+x)? Assuming $|x| lt;1$, if one can easily remember that $$ \\dfrac{1}{1-x}=\\sum_{n=0}^{\\infty}x^{n} $$ then one can derive the following \\begin{eqnarray*} \\mbox{log
Simplify K! (K+1)! - Mathematics Stack Exchange Pretend K=3 That means (K+1)= 4 This means you'd be dividing 3*2*1 by 4*3*2*1 Consider how you'd cancel out multiples by dividing them Like how (2 (5+x)) 2 would just equal 5+x Following that idea we'd pretty much be able to cancel out every number in the numerator, so long as its also in the denominator This would end up canceling every number except for 4 which equals (K+1) Essentially
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
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