2nd Imaginary Matrix Shrimp Sushi Restaurant Contest
Imaginary Matrix
$$ x^{2} = -1 \longrightarrow X^{2} = - E_{p} $$ The second contest addressed the Imaginary Matrix, a generalization of complex numbers to matrices as $\mathbb{R}^{p \times p}$.
Results
Participants included uriel, jryoungw, and Trakatus, with the scorecard available here.
Research
From the organizer’s perspective, a surprising aspect was the rapid rate of abstraction, sooner than expected. It was assumed that a winning strategy would involve initially exploring examples of imaginary matrices, identifying patterns, summarizing conditions, and then studying properties. However, research findings surged from the outset.
Significant highlights include:
- (22/05/03) uriel: Provided necessary and sufficient conditions for the existence of imaginary matrices based on size $p$ Link
- (22/05/04) Trakatus: Demonstrated that imaginary matrices possess only $\pm i$ as their eigenvalues Link
- (22/05/09) jryoungw: Explored the exponential form of imaginary matrices Link
- (22/05/10) Trakatus: Showed that all imaginary matrices are similar (extending to the complex domain) Link
- (22/05/11) uriel, Trakatus: Investigated the inner product of imaginary matrices Link1 Link2
- (22/05/15) jryoungw: Researched groups related to imaginary matrices Link
Competition
- Compared to the first contest, not only did participation increase by one, but the amount of research presented jumped to fifty-three theorems, observations, and critiques. For the next contest, we aim to simplify assumptions to make it more accessible.
- The highest individual scores were awarded for Trakatus’s “All eigenvalues of imaginary matrices are only $\pm i$” and jryoungw’s suggestion of specific groups of imaginary matrices, both receiving a perfect original score of 20 and an additional 8 points through citations.
- While the total duration was three months, most research occurred within the first two weeks.
Winners
- uriel with 202.8 points, winning 🥇 and 41,220 Won.
- jryoungw with 166.7 points, winning 🥈 and 33,880 Won.
- Trakatus with 122.5 points, winning 🥉 and 24,900 Won.
Fortunately, all three participants received prizes.
- jryoungw elected to decline the prize money, seeking a worthy cause for donation.
- uriel and Trakatus, please email your account details and competition feedback to freshrimpsushi@gmail.com.
🥈 Comments: jryoungw
I do not wish to receive the prize money. Please donate my winnings to a suitable cause.
This was my first foray into mathematics research, and I am grateful for this opportunity to open my mind to new ideas.
Sharing my thoughts, though brief and self-conscious, was enriching through discussions with others.
I look forward to more competitions in the future.
Thank you.
Sincerely, Jang Ryeongwoo
Epilogue
…
… Afterward, uriel and Trakatus were not seen again.