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IMA Journal of Mathematical Control and Information 1989 6(2):121-133; doi:10.1093/imamci/6.2.121
© 1989 by Institute of Mathematics and its Applications
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The Algebra of Matrices in N-dimensional Systems

N. M. SMART and S. BARNEIT

School of Mathematical Sciences, University of Bradford Bradford, BD7 1DP, U. K.

The N-dimensional Roesser matrix is defined and shown to be essential to the formal solution of the N-dimensional Roesser equations. An extended Cayley-Hamilton theorem and a Leverrier-Fadeev type algorithm are dervied for N-dminesional systems. One form of decomposition of the matrices is considered, and two particular cases are evaluated in terms of one-dimensional matrics.


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