Unverified50% confidenceFactExact time
The Laplace–Beltrami operator is the natural second-order differential operator on a manifold; on compact homogeneous spaces, its eigenfunctions are given by the matrix coefficients of irreducible representations, and its eigenvalues increase monotonically with the complexity of the representation (characterized by the highest weight).
1
Sources
50%
Confidence
Long-term
Relevance
10/12/2026
First Seen
Sources
Related Entities
Related Claims
UnverifiedThe name Cartesian derives from the Cartesian coordinate system, implying an emphasis on geometric precision and structured modeling.58% similarUnverified正交矩阵是列向量彼此正交且长度为1、满足UᵀU=I的方阵，在几何上代表旋转或反射操作，改变向量方向但不改变长度56% similarUnverified算子理论是泛函分析的核心分支，研究无穷维空间（如希尔伯特空间、巴拿赫空间）上的线性映射及其性质56% similarUnverifiedHadamard乘积是两个同维矩阵或张量对应位置元素相乘的运算，区别于矩阵乘法的行列点积56% similarUnverifiedThe Peter–Weyl theorem decomposes the space L^2(G) of square-integrable functions on a compact group into an orthogonal direct sum of subspaces spanned by the matrix coefficients of all irreducible unitary representations, with each irreducible representation appearing with a multiplicity equal to its dimension.55% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/1001362API
curl https://kongchang.com/api/v1/knowledge/claims/1001362MCP
get_claim(id=1001362)