Dirac Delta Function of Matrix Argument
Dirac Delta Function of Matrix Argument
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DOI：
10.1007/s10773-020-04598-8
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发表时间：
2016-07
影响因子：
1.4
通讯作者：
Lin Zhang
中科院分区：
文献类型：
--
作者：
Lin Zhang
矩阵辐角的狄拉克δ函数在随机矩阵理论、量子信息理论等领域的发展中经常被使用。本文的目的是教学，首先回顾了关于Heaviside单位阶跃函数和狄拉克δ函数的详细知识。然后分别系统地讨论了Dirac δ函数在向量空间和矩阵空间中的推广。给出了这些结果的详细和初步的证明。虽然我们还没有看到这些结果制定的文献中，肯定有前人。还提到了应用。例如，我们推导了（真实的和复）欧氏空间中两个独立随机单位向量的概率密度函数。
Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information Theory, etc. The purpose of the article is pedagogical, it begins by recalling detailed knowledge about Heaviside unit step function and Dirac delta function. Then its extensions of Dirac delta function to vector spaces and matrix spaces are discussed systematically, respectively. The detailed and elementary proofs of these results are provided. Though we have not seen these results formulated in the literature, there certainly are predecessors. Applications are also mentioned. For example, we derive the probability density functions of two independent random unit vectors in the (real and complex) Euclidean spaces.