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In [[mathematics]], a '''jacket matrix''' is a [[square symmetric matrix]] <math>A= (a_{ij})</math> of order ''n'' if its entries are non-zero and [[real number|real]], [[complex number|complex]], or from a [[finite field]], and [[File:Had_otr_jac.png|thumb|Hierarchy of matrix types]]
:<math>\ AB=BA=I_n </math>
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</math>
The jacket matrix is a generalization of the [[Hadamard matrix]]; it is a [[diagonal matrix|diagonal]] block-wise inverse matrix.
==Motivation==
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'''A'''·'''B''' = '''B'''·'''A''' = '''I'''
== Example 4. ==▼
▲== Example 4. ==
Consider <math>[\mathbf {A}]_N</math> be 2x2 block matrices of order <math>N=2p</math>
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[4] Moon Ho Lee, et. al., "MIMO Communication Method and System using the Block Circulant Jacket Matrix," US patent, no. US 009356671B1, May, 2016.
[5] S. K. Lee and M. H. Lee, “The COVID-19 DNA-RNA Genetic Code Analysis Using Information Theory of Double Stochastic Matrix,” IntechOpen, Book Chapter, April
==External links==
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* [https://web.archive.org/web/20110722132459/http://mdmc.chonbuk.ac.kr/english/images/Jacket%20matrix%20and%20its%20fast%20algorithm%20for%20wireless%20signal%20processing.pdf Jacket Matrix and Its Fast Algorithms for Cooperative Wireless Signal Processing]
* [https://www.researchgate.net/publication/342195507_Jacket_Matrices_-Construction_and_Its_Applications_for_Fast_Cooperative_Wireless_Signal_Processing: Jacket Matrices: Constructions and Its Applications for Fast Cooperative Wireless Signal Processing]
[[Category:Matrices]]
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