[數學普及] Measure Theory (測度論) 簡介 ver. 2

因為in呢個符號我比較難直接聯想返積分個基本concept
用sigma黎表達the sum of Infinitesimal
可能會比較易理解integration個概念

我唔係太明你個意思...?

Field theory 好難寫
會成個post都係linear algebra prerequisite

淨係知咩係dimension咪得

仲要知basis
即係要講linear independence

finite dimensional 好易姐, 應該唔駛點講 infinite extension 如果唔係你避唔到 axiom of choice

講埋曬啲off topic野會唔會悶親人

我已經懶唔define vector space

係finite dimensional喇
講Krull topology唔會有人睇

淨係講linear algebra都夠做一個post

field theory 淨係用到 chapter 1就ok
因爲基本上只係要用 dimension 的概念

我可以試下講下 (elementary) linear algebra 架, 易過 measure theory n 倍

咁少

如果你計埋applied LA係另外一回事
不如睇 horn & johnson算啦

講埋曬啲off topic野會唔會悶親人

我已經懶唔define vector space

係finite dimensional喇
講Krull topology唔會有人睇

淨係講linear algebra都夠做一個post

咁少

如果你計埋applied LA係另外一回事
不如睇 horn & johnson算啦

cholesky decomposition嗰啲計唔計

呢個應該係 numerical LA 果邊?
正常 LA 唔會教

Applied 嘅話, finite dim 都可以好深, 過晒elementary

最近有份paper講reverse cholesky

淨係 matrix theory 已經可以出幾本書啦

以我所知黎講, 至少8成做Quantum information 嘅research 都係finite dimensional setting, 講到尾都係matrix theory, matrix analysis, convex analysis, 但都係難到hihi咁

stat啲proof好多時都要用cholesky，spectral嗰堆decomposition

無知一問點reverse 應該唔係乘返埋佢?

https://lihkgmeasure.wordpress.com/
再推下, 更新到 Chapter 2
Chapter 2剩低的部份係比有 Analysis background的人睇, 可以跳左佢而又唔會影響閱讀

即係can be skipped without loss of continuity

如果你只係想知個 idea係點同呢個idea點樣tackle到 Riemann integral的問題唔駛睇呢D technical details

我覺得你將個textbook常用字眼譯咗幾得意啫

有時想要P=UU*, 而唔係P=LL*, 但喺infinite dim中, 唔係所有後者都可以decompose寫成為前者