Commun. Comput. Phys.,
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Volume 3.

Vector Addition Theorem and Its Diagonalization

W. C. Chew 1*

1 Faculty of Engineering, The University of Hong Kong, Hong Kong; and Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Urbana, IL 61801-2918, USA.

Received 6 March 2007; Accepted (in revised version) 22 May 2007
Available online 27 September 2007


The conventional vector addition theorem is written in a compact notation. Then a new and succinct derivation of the vector addition theorem is presented that is as close to the derivation of the scalar addition theorem. Newly derived expressions in this new derivation are used to diagonalize the vector addition theorem. The diagonal form of the vector addition theorem is important in the design of fast algorithms for computational wave physics such as computational electromagnetics and computational acoustics.

AMS subject classifications: 43A45, 43A65, 43A90, 47L90, 78M99
PACS: 03.50.De, 85.40.Bh, 89.20.Ff
Key words: Addition theorem, vector field, fast algorithm, electromagnetic theory.

*Corresponding author.
Email:, (W. C. Chew)

The Global Science Journal