Department Seminars and Colloquium
Carl-Fredrik Nyberg Brodda (KIAS)Topology Seminar
An invitation to combinatorial semigroup theory III
Carl-Fredrik Nyberg Brodda (KIAS)Topology Seminar
An invitation to combinatorial semigroup theory IV
박종일 (서울대학교)Topology Seminar
A study on rational homology projective planes
Taeyoon Woo (KAIST)Etc.
Grothendieck groups of regular schemes 1
엄기윤 (KAIST)Differential Geometry
On partition functions of determinantal point processes on polarized Kähler manifolds
Graduate Seminars
SAARC Seminars
PDE Seminars
Ioan Bejenaru (UC San Diego)Partial Differential Equations
Global well-posedness and scattering for the massive Dirac-Klein-Gordon system in two dimensions.
은남현 (KAIST)Partial Differential Equations
Existence and uniqueness of global strong solutions for one-dimensional compressible navier-stokes equations
IBS-KAIST Seminars
Conferences and Workshops
Student News
Bookmarks
Research Highlights
Bulletin Boards
Problem of the week
Let \( X \in \mathbb{R}^{n \times n} \) be a symmetric matrix with eigenvalues \( \lambda_i \) and orthonormal eigenvectors \( u_i \). The spectral decomposition gives \( X = \sum_{i=1}^n \lambda_i u_i u_i^\top \). For a function \( f : \mathbb{R} \to \mathbb{R} \), define \( f(X) := \sum_{i=1}^n f(\lambda_i) u_i u_i^\top \). Let \( X, Y \in \mathbb{R}^{n \times n} \) be symmetric. Is it always true that \( e^{X+Y} = e^X e^Y \)? If not, under what conditions does the equality hold?
KAIST Compass Biannual Research Webzine
Let \( X \in \mathbb{R}^{n \times n} \) be a symmetric matrix with eigenvalues \( \lambda_i \) and orthonormal eigenvectors \( u_i \). The spectral decomposition gives \( X = \sum_{i=1}^n \lambda_i u_i u_i^\top \). For a function \( f : \mathbb{R} \to \mathbb{R} \), define \( f(X) := \sum_{i=1}^n f(\lambda_i) u_i u_i^\top \). Let \( X, Y \in \mathbb{R}^{n \times n} \) be symmetric. Is it always true that \( e^{X+Y} = e^X e^Y \)? If not, under what conditions does the equality hold?