International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Matrix Dimensional Analysis for Electromagnetic Quantities

Matrix Dimensional Analysis for Electromagnetic Quantities

Mostafa Ali Rushdi
Faculty of Engineering and Technology, Future University in Egypt (FUE), New Cairo, 11835, Arab Republic of Egypt. (Currently with Interdisciplinary Graduate School of Engineering Sciences (IGSES), Earth System Science and Technology (ESST), Kyushu University, Fukuoka, 816-8580, Japan).

Ali Muhammad Rushdi
Department of Electrical and Computer Engineering, King Abdulaziz University Jeddah 21589, Kingdom of Saudi Arabia.

DOI https://doi.org/10.33889/IJMEMS.2021.6.2.039

Received on September 22, 2020
Accepted on January 02, 2021


We utilize the electromagnetically-oriented LTI∅ dimensional basis in the matrix solution of dimensional-analysis (DA) problems involving mainly electromagnetic quantities, whether these quantities are lumped or distributed. Representations in the LTI∅ basis (compared with the standard MLTI basis) are more informative and much simpler. Moreover, matrix DA computations employing the LTI∅ basis are more efficient and much less error prone. Extensive discussions of two demonstrative examples expose technical details of a novel DA scheme, and clarify many important facets of modern dimensional analysis.

Keywords- Dimensional analysis, Gauss-Jordan algorithm, Bases and regimes, Electromagnetics, Duality, The LTI∅ basis, The MLTI basis.


Rushdi, M. A., & Rushdi, A. M. (2021). Matrix Dimensional Analysis for Electromagnetic Quantities. International Journal of Mathematical, Engineering and Management Sciences, 6(2), 636-644. https://doi.org/10.33889/IJMEMS.2021.6.2.039.

Conflict of Interest

The authors assert that no conflict of interest exists.


The authors are greatly indebted to Dr. Ahmad Ali Rushdi for the technical help he generously and proficiently offered during the preparation of this manuscript. They are really appreciative of his perseverance and his expertise.


Bhaskar, R., & Nigam, A. (1990). Qualitative physics using dimensional analysis. Artificial Intelligence, 45(1-2), 73-111.

Buckingham, E. (1914). On physically similar systems: illustrations of the use of dimensional equations. Physical Review, 4(4), 345-376.

Chen, W.K. (1971). Algebraic theory of dimensional analysis. Journal of the Franklin Institute, 292(6), 403-422.

Hutter, K., & Jöhnk, K. (2004). Theoretical foundation of dimensional analysis. In Continuum Methods of Physical Modeling (pp. 339-392), Springer, Berlin, Heidelberg.

Kinitsky, V.A. (1962). Kalantaroff dimension system. American Journal of Physics, 30(2), 89-93.

Middendorf, W.H. (1986). The use of dimensional analysis in present day design environment. IEEE Transactions on Education, E-29(4), 190-195.

Oladigbolu, J.O., & Rushdi, A.M.A. (2020). Investigation of the corona discharge problem based on different computational approaches of dimensional analysis. Journal of Engineering Research and Reports, 15(3), 17-36.

Palanthandalam-Madapusi, H.J., Bernstein, D.S., & Venugopal, R. (2007). Dimensional analysis of matrices state-space models and dimensionless units [Lecture Notes]. IEEE Control Systems Magazine, 27(6), 100-109.

Rushdi, M.A., & Rushdi, A.M. (2016). [Short Note]: On the fundamental masses derivable by dimensional analysis. Journal of King Abdulaziz University, Engineering Sciences, Jeddah, 27(1), 35-42.

Rushdi, M.A., & Rushdi, A.M. (2020a). Modeling virus spread rate via modern techniques of dimensional analysis. Journal of King Abdulaziz University: Computing and Information Technology Sciences, 9(2), 47-66.

Rushdi, M.A., & Rushdi, A.M. (2020b). Modeling coronavirus spread rate utilizing dimensional analysis via an irredundant set of fundamental quantities. International Journal of Pathogen Research, 5(3), 8-21.

Szirtes, T. (2007). Applied dimensional analysis and modeling. Second Edition, Butterworth Heinemann, Burlington, MA, USA.

Young, L. (1957). Electrical units and dimensions Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics, 75(6), 767-771.