https://log.zxcvber.com/CSE & Math & Life 2026-02-10T15:03:15+09:00 Sungchan Yi https://log.zxcvber.com/ Jekyll © 2026 Sungchan Yi /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png 2026-01-02T00:00:00+09:00 2026-01-02T00:00:00+09:00 https://log.zxcvber.com/mathematics/algebra/2026-01-02-matmul-as-tensors/ Sungchan Yi

Introduction Matrices have various applications throughout many fields of science. However, when we first learn matrices and their operations, the most non-intuitive concept is the multiplication of matrices. Compared to addition and scalar multiplication, which are very intuitive, matrix multiplication has a rather strange definition. Definition. (Matrix Multiplication) For $A = (a _ {ij...

2025-08-22T00:00:00+09:00 2025-08-22T23:26:02+09:00 https://log.zxcvber.com/mathematics/2025-08-22-group-structure-of-z-2n-z-star/ Sungchan Yi

To compute the rotation automorphism homomorphically, we use the fact that $(\Z/2^n\Z)^* \simeq \span{-1, 5}$. I couldn’t find a clear proof of this result online, so I just accepted the fact although it wasn’t very satisfying. After more than a year, I got a chance to revisit the rotation automorphism and I figured that I should clear things up once and for all. So I decided to compile a proo...

2024-11-17T00:00:00+09:00 2024-11-17T09:26:47+09:00 https://log.zxcvber.com/development/web/2024-11-17-math-equations-in-markdown/ Sungchan Yi

마크다운에서 수식을 사용하는 것은 생각보다 어렵다. 애초에 마크다운은 원래 수식을 지원하지 않는다. 그저 Github, Obsidian 등 다양한 플랫폼이 마크다운의 확장 형태로 수식 입력을 지원하고 있는 상황이다. 이 블로그는 jekyll을 사용하기 때문에 모든 글이 마크다운으로 작성되어 있다. 수학을 좋아하는 나의 특성상 블로그 글에 수식을 입력할 일이 많은데, 어느 날 블로그에서 깨져있거나 잘못된 수식을 발견하고 마크다운에서 수식을 사용하는 것이 그리 간단치 않다는 것을 깨닫게 되었다. 이 글에서는 마크다운에서 수식을 사용할 때 생기는 문제점과 이에 대한 해결책을 정리했다. 문법의 충돌 마크다운 엔진에 따라 구체적인 내용이 다를 수도 있지만, Kramdown의 경우 문법이 충돌하는 대표적인...

2024-04-12T00:00:00+09:00 2024-04-12T00:00:00+09:00 https://log.zxcvber.com/algorithms/data-structures/2024-04-12-search-time-hash-tables/ Sungchan Yi

Here are the expected time complexities of the search operation in hash tables. Assumptions Let $m$ be the number of buckets in the hash table. Let $n$ be the number of entries currently in the hash table. Let $\alpha = n/m$ be the load factor. Elements are uniformly hashed to each bucket of the hash table. These results imply that the search operation takes almost constant time. ...

2024-03-11T00:00:00+09:00 2024-03-11T00:00:00+09:00 https://log.zxcvber.com/articles/2024-03-11-you-and-your-research/ Sungchan Yi

Link to original text. I recommend reading the full text. It may seem a bit long but I assure you that it is worth the time. The talk is mainly about how to do first-class work, something significant as a great scientist. The following is a list of quotes from the text that inspired me. Bold fonts were not in the original text, I added them on my own. Read the full text for the full cont...