Some Classroom Comments on Bilinear Transformations
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Taylor expansions and subsequent arrangement in linear simultaneous-equation form lead to matrices for the numerical application of the bilinear transformation z=(s+1)/(s-1). The matrices are somewhat similar to those previously reported, but the proof seems more adaptable to the classroom.
[1] Henry M. Power,et al. The Mechanics of the Bilinear Transformation , 1967 .