Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space.
Mathematical Background.- Group Theory.- Rings.- Matrices and linear equations systems.- Permutations and Determinants.- Vector and Euclidean Spaces.- Linear Transformations.- Matrix Diagonalization and Jordan Canonical Form.- Differential Equations.- Differential Algebra for Nonlinear Control Theory.- Appendix.- Index.
“The book is an introduction to the mathematical tools of control theory, and specifically the differential algebraic approach, for readers with no previous background in this field.” (Filippo Cacace, Mathematical Reviews, October, 2019)