In my previous post, I introduced various definitions of matrix norms in \(\mathbb{R}^{n \times n}\) based on the corresponding vector norms in \(\mathbb{R}^n\). Meanwhile, the equivalence of different vector norms and their induced metrics and topol…
Proof of Theorem 20.3 Theorem 20.3 The topologies on \(\mathbb{R}^n\) induced by the euclidean metric \(d\) and the square metric \(\rho\) are the same as the product topology on \(\mathbb{R}^n\). Proof: a) Prove the two metrics can mutually limit ea…
http://scottsievert.github.io/blog/2015/01/31/the-mysterious-eigenvalue/ The Fibonacci problem is a well known mathematical problem that models population growth and was conceived in the 1200s. Leonardo of Pisa aka Fibonacci decided to use a recursiv…
第二周 第一部分 Multivariate Linear Regression Multiple Features Note: [7:25 - θT is a 1 by (n+1) matrix and not an (n+1) by 1 matrix] Linear regression with multiple variables is also known as "multivariate linear regression". We now introduce notatio…
