[9up數學] 咩叫維度? (數學角度)

數學女孩

會唔會講下Mandelbrot

關佢咩事

無咩事我返出去等睇topology個post先啦

應該聽日會得閒D出post

推

睇明小小, 唔明好多, 輕輕一推

我諗大部份人會明vector space果個, 後面果兩個我唔expect non-math major會明

其實講fractal dimension有D唔準確, 因爲玩fractal可以有好多種dimension, 例如box-counting dimension, packing dimension, 同埋我上面提ge Hausdorff dimension等等
Hausdorff dimension係我地平時諗的dimension ge extension黎, 如果係open set, 個Hausdorff dimension同佢本身個dimension (as manifold or topological) 會一樣

簡單來講4維空間等於4條線互相垂直
暗示4個參數互相彼此獨立

無inner product structure講乜垂直

想問下
無inner product 係咪
1. 無得講垂直/角度？
2. 無metric？
3. 但都可以講平行？

1. inner product就係measure of angle, 又或者你提供一個rigorous definition of orthogonality without inner product.

2. no, R^n 但用 p-norm (p =/= 2) 唔係inner product space

3. parallel 本身係指兩枝vector係linearly dependent, 呢樣唔駛inner product都define到

btw
一個normed space ge norma幾時係induced by some inner product可以參考條link

https://math.stackexchange.com/questions/21792/norms-induced-by-inner-products-and-the-parallelogram-law