Transversality theorem: a useful tool for establishing genericity

It is demonstrated, by way of examples in linear algebra and control, optimization, and geometry, that the transversality theorem of differential topology is a very useful tool for establishing the genericity of a property which is dependent on a finite number of real parameters and which is expressible using a system of nonlinear equations. Some of the results derived are nontrivial to establish by direct means without resorting to the use of the transversality theorem.<
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