This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing, covering the necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms along the way. It will appeal to advanced undergraduate and first-year graduate students, research mathematicians and statisticians.

Vector Spaces and Matrices.- Linear Estimation.- Tests of Linear Hypotheses.- Singular Values and Their Applications.- Block Designs and Optimality.- Rank Additivity.