Dirac Delta Function of Matrix Argument

Abstract

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.

26 pages, LaTeX, no figures. Any comments are welcome!. arXiv admin note: text overlap with arXiv:quant-ph/0012101 by other authors

References in corpus (4)

• The difference between two random mixed quantum states: exact and asymptotic spectral analysis
• Average coherence and its typicality for random mixed quantum states
• Volume of the space of qubit-qubit channels and state transformations under random quantum channels
• Incompatibility probability of random quantum measurements

Cited by in corpus (3)

• Uncertainty regions of observables and state-independent uncertainty relations
• Probability density functions of quantum mechanical observable uncertainties
• On a Matrix Ensemble for Arbitrary Complex Quantum Systems