Extending and applying properties of the uc generalized matrix inverse
The recent development of a generalized matrix inverse which preserves the units of state variables is very important for many areas of science and technology. In this thesis we derive new mathematical results for this inverse and prove that it offers a unified solution to replace ad hoc approaches that were needed before the new inverse became available. We begin by introducing the existing problem when a generalized inverse must be used in a system with parameters defined in incommensurate units. We test the hypothesis that the new inverse can replace special-purpose methods in robotics and control systems and we show through simulations that the new approach is not only mathematically more elegant but also significantly more efficient to compute. Additionally, we prove new properties of the new inverse involving the Kronecker matrix product and show how the new inverse can be mixed with other generalized inverses to solve more complex systems.
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