The purpose of this paper is to provide necessary and sufficient conditions on a continuous and matrix valued radial kernel on a Euclidean space in order that it be conditionally positive definite of a fixed order. Except for the one dimensional Euclidean space, the strict conditional positive definiteness of the kernel is fully characterized.

中文翻译：

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欧几里德空间上的条件正定矩阵值核

本文的目的是提供欧几里德空间上连续的矩阵值径向核的充分必要条件，使其成为固定阶数的条件正定。除一维欧几里得空间外，核的严格条件正定性得到充分表征。