## Proof that projection matrix P has lambda = 0 and lambda = 1

Assume that is an eigenvector of . Then has atmost two eigenvalues (0 or 1).     Prove that there exists an eigenvector of with eigenvalue equals 1: We have , therefore we can pick any column vectors of and it will be an eigenvector of with eigenvalue equals 1. Prove that there exists an [...]

## [Notes] Cracking the GRE Mathematics Subject Test – Steve Leduc

Page 172: http://farside.ph.utexas.edu/teaching/sm1/lectures/node36.html#e4.32

## An intuition to an tangent plane to a surface

To me: Page 126 of Cracking the GRE Math Subject Test. A rigorous proof can be found here (Calculus, Howard Anton). A note of stress should be on “any smooth curve C on the surface”. Below is my attempt interpretation before looking at any proofs. While it cannot be considered as a proof, it shows [...]

## Proof of lower-rank matrix factorization

Let and and  , prove that . We can determine  by applying row operations on . First, we will let the second row of  after the first row operation be: . Next, the third row of  after the second row operation would be: . Soon, we will come to () which is a linear combination [...]

## Entropy 2016, bảng A

It took me quite a lot of time to understand the question, though. I do not post the test here as I am not sure if I am permitted to do that. This post serves for my personal use. Even though the original questions are written in Vietnamese, I will be writing my solutions in [...]

## IELTS Writing 5 Days Challenge

Wealthy nations should assist poorer countries with humanitarian relief during natural disasters. Do you agree or disagree? It is argued that rich countries should offer financial help to developing nations while they are suffering from natural disasters such as earthquake, storm, and flood. This essay agrees with the statement because wealthy nations have the ability [...]