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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∥ ...

Inverse of the sum of matrices - Mathematics Stack Exchange
The technique is useful in computation, because if the values in A and B can be very different in size then calculating 1 A+B 1 A + B $\frac{1}{A+B}$ according to (3) (3)

一个最大值大于1的概率密度函数的意义是什么? - 知乎
题主应该是把 概率质量函数 (probability mass function)和 概率密度函数 (probability density function)搞混了。 概率质量函数的取值确实无法大于1,但概率密度函数则不然。 以下内容搬运自维基百科: 在概率论中,概率质量函数是离散随机变量在各特定取值上的概率。

1-1+1-1+1-1+1... 这个无穷数列的值是什么?如何证明? - 知乎
知乎,中文互联网高质量的问答社区和创作者聚集的原创内容平台,于 2011 年 1 月正式上线,以「让人们更好的分享知识、经验和见解,找到自己的解答」为品牌使命。

Easy way to remember Taylor Series for log (1+x)?
Assuming $|x|<1$, 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 ...

Why is $1/i$ equal to $-i$? - Mathematics Stack Exchange
Why is 1/i 1 / i $1/i$ equal to −i i $-i$? Ask Question Asked 11 years, 5 months ago Modified 1 year, 9 months ago Viewed 118k times 67

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.

Product of slopes is -1 iff perpendicular proof from first principles
To do this from "first principles", one would need to know the definition of "perpendicular".

 

 

 

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