a common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the weierstrass canonical form. the weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. the present ...

The variety of uniform matrix product states arises both in algebraic geometry as a natural generalization the Veronese variety, and quantum many-body physics model for translation-invariant system sites placed on ring. Using methods from linear algebra, representation theory, invariant theory matrices, we study span this variety.