Let A, B be Hermitian matrices. Prove that tr(A2B2) ≥ tr((AB)2).
Monthly Archives: October 2010
Break for the midterm exam
KAIST POW will take a break for the midterm exam. Good luck to all students!
Next problem will be posted on Oct. 29th.
Solution: 2010-16 Number of divisors in 1 (mod 3) or 2 (mod 3)
Let n be a positive integer. Let D(n,k) be the number of divisors x of n such that x≡k (mod 3). Prove that D(n,1)≥D(n,2).
The best solution was submitted by Jeong, Seong Gu (정성구), 수리과학과 2007학번. Congratulations!
Here is his Solution of Problem 2010-16.
Alternative solutions were submitted by 정진명 (수리과학과 2007학번, +3), 김치헌 (수리과학과 2006학번, +3), 박민재 (KSA-한국과학영재학교, +3).
2010-16 Number of divisors in 1 (mod 3) or 2 (mod 3)
Let n be a positive integer. Let D(n,k) be the number of divisors x of n such that x≡k (mod 3). Prove that D(n,1)≥D(n,2).
Solution: 2010-15 Characteristic Polynomial
Let A, B be 2n×2n skew-symmetric matrices and let f be the characteristic polynomial of AB. Prove that the multiplicity of each root of f is at least 2.
The best solution was submitted by Chiheon Kim (김치헌), 수리과학과 2006학번. Congratulations!
Here is his Solution of Problem 2010-15.
An alternative solution was submitted by 정진명 (수리과학과 2007학번, +2).
2010-15 Characteristic Polynomial
Let A, B be 2n×2n skew-symmetric matrices and let f be the characteristic polynomial of AB. Prove that the multiplicity of each root of f is at least 2.