## 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 [...]

Present a written argument or case to an educated reader with no specialist knowledge of the following topic. It is important for children to learn the difference between right and wrong at an early age. Punishment is necessary to help them learn this distinction. To what extent do you agree or disagree with this opinion? [...]

The first chart below shows how energy is used in an average Australian household. The second chart shows the greenhouse gas emissions which result from this energy use. Summarise the information by selecting and reporting the main features, and make comparisons where relevant. The first pie chart illustrates the proportion of energy use whilst the [...]

## How to highlight column and row of your active cell in Excel 2016

Words of caution: I’m no VBA expert, use the code at your own risk. Credits and References: Hightlight active row/column in Excel without using VBA? Force a screen update in Excel VBA Application.ScreenUpdating can dramatically speed up your code (please do not be misled by the title) You can google more about how to apply VBA code in [...]

## Triplet Loss’ derivative of VGG Face

We starts with the formula (1) of the paper.     We have:             By chain rule, we have:     We also have: – the th element of .   – the th element of . So:

## [Notes] Learning From Data – A Short Course: e-Chapter 9

Page 30: Why ? My understanding:   as the events and are independent, the same goes for the event . Note that both data points and may exist in dataset so if is a deterministic hypothesis then it is obviously  as . If is a non-deterministic hypothesis,  is still independent from the random target function (even “ are [...]