General Information
    • ISSN: 1793-8201 (Print), 2972-4511 (Online)
    • Abbreviated Title: Int. J. Comput. Theory Eng.
    • Frequency: Quarterly
    • DOI: 10.7763/IJCTE
    • Editor-in-Chief: Prof. Mehmet Sahinoglu
    • Associate Editor-in-Chief: Assoc. Prof. Alberto Arteta, Assoc. Prof. Engin Maşazade
    • Managing Editor: Ms. Mia Hu
    • Abstracting/Indexing: Scopus (Since 2022), INSPEC (IET), CNKI,  Google Scholar, EBSCO, etc.
    • Average Days from Submission to Acceptance: 192 days
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Prof. Mehmet Sahinoglu
Computer Science Department, Troy University, USA
I'm happy to take on the position of editor in chief of IJCTE. We encourage authors to submit papers concerning any branch of computer theory and engineering.

IJCTE 2019 Vol.11(6): 107-111 ISSN: 1793-8201
DOI: 10.7763/IJCTE.2019.V11.1252

Finding the Unique Permutation Matrix for Reverse Order Kronecker Product Intuitively

Muhammad G. Ali, Shoab A. Khan, and Sajid G. Khawaja

Abstract—With the adverse research in field of engineering and technology, the use of Kronecker product highlighted from many aspects by researchers in different fields of science, especially considering digital signal processing where Discrete Fourier Transform plays a supreme role. This transform can be performed using Kronecker product in an iterative way. The implementation of DFT using this product needs a reverse order multiplication that can easily be catered for by applying few techniques of linear algebra i.e. by using a unique permutation matrix, on the original Kronecker Product. The permutation matrix obtained from “I” interchanging of rows / columns from an identity matrix. A total of n! permutation matrices will be obtained using this methodology. This paper presents a technique for finding the unique permutation matrix out of n! matrices. This uniquely identified permutation matrix is used to attain the reverse order Kronecker product without using the same technique, as used for obtaining the original Kronecker product.

Index Terms—Discrete fourier transform (DFT), digital signal processing (DSP), intuitive method, kronecker product (KP), permutation matrix (PM).

Muhammad G. Ali, Shoab A. Khan, and Sajid G. Khawaja are with Department of Computer Engineering, College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Pakistan (e-mail:,,


Cite:Muhammad G. Ali, Shoab A. Khan, and Sajid G. Khawaja, "Finding the Unique Permutation Matrix for Reverse Order Kronecker Product Intuitively," International Journal of Computer Theory and Engineering vol. 11, no. 6, pp. 107-111, 2019.

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