2 comments about Matrices for Statistics.

1. This book gives a very concise treatment fo matrix algebra, covering from first principles the basic mathematics. It is oriented toward statistical applications such as the least squares solution in regression, concepts of principal components and other multivariate statistical topics where matrices play an important role. I particularly like the way determinants were introduced and motived by the generalization of "never divide by zero." It is a good reference for statistical practitioners including statisticians, engineers, biologists and social scientists. For those interested in a more thorough treatment there are other noteworthy books, one by Searle and one by Graybill. Healy's text is inexpensive and easy to use as a reference particularly the paperback edition that I have.



2. This book gives a very concise treatment fo matrix algebra, covering from first principles the basic mathematics. It is oriented toward statistical applications such as the least squares solution in regression, concepts of principal components and other multivariate statistical topics where matrices play an important role. I particularly like the way determinants were introduced and motived by the generalization of "never divide by zero." It is a good reference for statistical practitioners including statisticians, engineers, biologists and social scientists. For those interested in a more thorough treatment there are other noteworthy books, one by Searle and one by Graybill. Healy's text is inexpensive and easy to use as a reference particularly the paperback edition that I have.

No comments about Matrix Theory and Applications with MATLAB.

1 comments about Theory of Matrices.

1. This is a self-contained and extremely well-written and clear exposition of matrix theory primarily from the viewpoint of matrix polynomials. The proofs are all clear and easy to follow without sacrificing completeness. I would recommend reading this book before reading Theory of Matrices by Lancaster and Tismenetsky.

No comments about Non-negative Matrices and Markov Chains (Springer Series in Statistics).

3 comments about A Survey of Matrix Theory and Matrix Inequalities.

1. This book is not really a review of matrix theory; the focus is on inequalities, mainly for PD matrices, convex functions and eigenvalue problems. The book tries to present a general framework, a-la Hardy, but is not quite as successful. Nevertheless, if you need to find that elusive inequality that you saw in undergraduate, this book will likely contain it. This book should be on every mathematical researcher's shelf.



2. I have just read part I of the book (table of contents below), and I like it very much. So many information, on so few pages. Everything is threated in FULL generality, and proves are included for the main theorems. This book has also an excellent encyclopedia function, as it contains the main properties of anything that one can think of.

   Beware: I have some mathematical background, and if you fully want to appreciate this book you will need this. (don't buy this book if this would be your first confrontation with matrices).

   Table of contents:

   I Survey of matrix theory
   1 Introductory concepts
   2 Numbers associated with matrices
   3 Linear equations and canonical forms
   4 Special classes of matrices, commutativity
   5 Congruence

   II Convexity and matrices
   1 Convex sets
   2 Convex functions
   3 Classical Inequalities
   4 Convex functions and matrix inequalities.
   5 Nonnegative matrices

   III Localization of characteristic roots
   1 Bounds for characteristic roots
   2 Regions containing characteristic roots of a general matrix
   3 Characterstic roots of a general matrix
   4 The spread of a matrix
   5 The field of values of a matrix




3. Each section starts with a set of necessary definitions. Then, theorems are stated without proof---therefore, the it can also be used as an exercise book. One can go to a section of interest and try to prove some of the theorems listed there.

1 comments about Matrices, Geometry & Mathematica.

1. Mathematica based tutorial built largely around Singular Value Decomposition analysis. Gives a very solid intuitive understanding of the subject.

1 comments about The Theory of Matrices in Numerical Analysis (Dover Books on Mathematics).

1. Table of contents
   
   1. SOME BASIC IDENTITIES AND INEQUALITIES
   1.0 Objectives; Notation
   1.1 Elementary Matrices
   1.2 Some Factorizations
   1.3 Projections, and the General Reciprocal
   1.4 Some Determinantal Identities
   1.5 Lanczos Algorithm for Tridiagonalization
   1.6 Orthogonal Polynomials
   References
   Problems and Exercises
   
   2. NORMS, BOUNDS, AND CONVERGENCE
   2.0 The Notion of a Norm
   2.1 Convex Sets and Convex Bodies
   2.2 Norms and Bounds
   2.3 Norms, Bounds, and Spectral Radii
   2.4 Nonnegative Matrices
   2.5 Convergence; Functions of Matrices
   References
   Problems and Exercises
   
   3. LOCALIZATION THEOREMS AND OTHER INEQUALITIES
   3.0 Basic Definitions
   3.1 Exclusion Theorems
   3.2 Inclusion and Separation Theorems
   3.3 Minimax Theorems and the Field of Values
   3.4 Inequalities of Wielandt Kantorovich
   References
   Problems and Exercises
   
   4. THE SOLUTION OF LINEAR SYSTEMS: METHODS OF SUCCESSIVE APPROXIMATION
   4.0 Direct Methods and Others
   4.1 The Inversion of Matrices
   4.2 Methods of Projection
   4.3 Norm-Reducing Methods
   References
   Problems and Exercises
   
   5. DIRECT METHODS OF INVERSION
   5.0 Uses of the Inverse
   5.1 The Method of Modification
   5.2 Triangularization
   5.3 A More General Formulation
   5.4 Orthogonal Triangularization
   5.5 Orthogonalization
   5.6 Orthogonalization and Projection
   5.7 The Method of Conjugate Gradients
   References
   Problems and Exercises
   
   6. PROPER VALUES AND VECTORS: NORMALIZATION AND REDUCTION OF THE MATRIX
   6.0 Purpose of Normalization
   6.1 The Method of Krylov
   6.2 The Weber-Voetter Method
   6.3 The Method of Danilevskii
   6.4 The Hessenberg and the Lanczos Reductions
   6.5 Proper Values and Vectors
   6.6 The Method of Samuelson and Bryan
   6.7 The Method of Leverrier
   References
   Problems and Exercises
   
   7. PROPER VALUES AND VECTORS: SUCCESSIVE APPROXIMATION
   7.0 Methods of Successive Approximation
   7.1 The Method of Jacobi
   7.2 The Method of Collar and Jahn
   7.3 Powers of a Matrix
   7.4 Simple Iteration (the Power Method)
   7.5 Multiple Roots and Principal Vectors
   7.6 Staircase Iteration (Treppeniteration)
   7.7 The LR-Transformation
   7.8 Bi-iteration
   7.9 The QR-Transformation
   References
   Problems and Exercises
   
   BIBLIOGRAPHY
   INDEX

No comments about Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics).

No comments about Matrix and Tensor Calculus: With Applications to Mechanics, Elasticity and Aeronautics.

No comments about Matrices and Quadratic Forms.