2016年6月9日 · NB the definitions of sgn(0) sgn ⁡ (0) vary between 0 0 and 1 1. If 0 0 is a plausible argument, you should assure yourself of the definition of sgn sgn at 0 0 in your context.

sgn (x) 在求导和积分中可以看作是常数 并不完全严谨，至少不能真的当成一个k值提出；它本质是个分段函数，在不同区间取值不同。

阶跃函数，数学上的符号函数或者计算机语言中的返回函数。Sgn 函数 返回一个 Variant (Integer)，指出参数的正负号。 语法 Sgn (number) 必要的 number 参数是任何有效的数值表达式。

The sign of a permutation σ ∈Sn σ ∈ S n, written sgn(σ) s g n (σ), is defined to be +1 if the permutation is even and -1 if it is odd, and is given by the formula

2017年9月17日 · You know that sgn(x) =⎧⎩⎨1 0 −1 x> 0 x = 0 x <0 s g n (x) = {1 x> 0 0 x = 0 − 1 x <0 I think you can get the derivative from there, derivate each piece of the function. Notice the discontinuity points and consider how this affects the existence of derivative at some points.

2021年3月11日 · Using only the arithmetic operations, the identity function and the absolute value, this does not seem possible, because the sgn sgn function is discontinuous. As far as I see, a discontinuity can only appear with a division by zero, which results in an undefined value in at least one point.

The hard part of sgn s g n is to show that any transposition decomposition of a permutation will always have an odd number or and even number of transposition, regardless of how you decompose it--you can have as many transpositions as you want, even more than n n transpositions. So you assign permutations with an even number of transpositions 1 and …

Pay attention to the fact that in the formula in (1) (1) , for any 1 ≤ i <j ≤ n 1 ≤ i <j ≤ n, the denominator j − i j − i is always positive , so what "decides" the sign there is merely the numerator σ(j) − σ(i) σ (j) − σ (i) , thus: both "definitions" you wrote down of sgn are exactly the same. Now, let us write down the given information:

Alternatively you can show that sgn sgn factors through the group of n × n n × n permutation matrices using the determinant map. Since det det is a homomorphism we get the result.

2021年2月18日 · Please don't edit sgn to sin. I mean sgn as a sign function not as sine.