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The recent developments in canonical transforms, matrix theory, block Kronecker multiplications, and other areas are applied to extend and simplify results in the theory of first order systems and special relativity. Especially noteworthy are the author's results on Fourier transforms in dimensions lower than the surrounding space and his approach to the Doppler effect, which has never been published previously and supersedes previous work on this topic, which failed to solve the Doppler effect exactly. Some of the goals of this work are: to develop the theory of complex symmetric matrices as...