Finite Zeros in Discrete Time Control Systems Zeros and the Output Zeroing Problem A General Solution to the Output Zeroing Problem The Moore Penrose Inverse of the First Markov Parameter Singular Value Decomposition of the First Markov Parameter Output Nulling Subspaces in Strictly Proper Systems Output Nulling Subspaces in Proper Systems Singular Systems. A state space approach to the analysis of zeros of MIMO LTI discrete time systems is presented. The basic mathematical tools used in this analysis are the Moore Penrose pseudoinverse and singular value decomposition of the first nonzero Markov parameter of a system. The book starts with definition of invariant zeros and goes as far as a general characterization of output zeroing inputs and the corresponding solutions explicit formulas for maximal output nulling invariant subspaces and for the zero dynamics. The objective of this book is to render the reader familiar with a certain method of analysis of multivariable zeros (which goes beyond the classical approach) and related problems. The minimal mathematical background that is required from the reader is a working knowledge of linear algebra and difference equations. The reader should be familiar with the basic concepts of linear system theory.