Search
Search Results
-
Matrix Algebra Theory, Computations and Applications in Statistics
This book presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and...
-
Matrix Transformations and Factorizations
In most applications of linear algebra, problems are solved by transformations of matrices. A given matrix (which represents some transformation of a...
-
Matrix Algebra, Probability and Statistics
The necessary mathematical background for the textbook is reviewed in this chapter. This includes second year calculus, matrix algebra, probability...
-
Matrix Calculus
When we deal with many variables, the designation of a variable by a subscript becomes cumbersome. Once we introduce the matrix notation, the...
-
Matrix Algebra
Matrix algebra is an important step in mathematical treatment of shrinkage estimation for matrix parameters, and in particular the Moore-Penrose...
-
Software for Numerical Linear Algebra
There is a variety of computer software available to perform the operations on vectors and matrices discussed in Chap. 11 and previous chapters. I...
-
Numerical Linear Algebra
Many scientific computational problems in various areas of application involve vectors and matrices. Programming languages such as C provide the...
-
Some Linear Algebra
MANY OPERATIONS performed on multivariate data are facilitated using vector and matrix notation. In this chapter, we introduce the basic operations...
-
Professor Heinz Neudecker and matrix differential calculus
The late Professor Heinz Neudecker (1933–2017) made significant contributions to the development of matrix differential calculus and its applications...
-
Selected Matrix Algebra Topics and Results
This chapter presents exercises on selected matrix algebra topics and results and provides solutions to those exercises.
-
Selected Matrix Algebra Topics and Results
Before we can begin to tackle the inference problems described near the end of the previous chapter, we must first develop an adequate working...
-
Jones-Balakrishnan Property for Matrix Variate Beta Distributions
Let
X andY be independent m × m symmetric positive definite random matrices. Assume thatX follows a matrix variate beta distribution with... -
Background: Linear Algebra
We will begin our course of study by reviewing the most relevant definitions and concepts of linear algebra. We will also expand on various aspects...
-
Some Introductory Algebra
In this chapter, we summarize some basic theory concerning permutations, multilinear algebra, set partitions, and diagrams for usage throughout the...
-
Compositional Data Analysis—Linear Algebra, Visualization and Interpretation
Compositional data analysis is concerned with multivariate data that have a constant sum, usually 1 or 100%. These are data often found not only in...
-
Measuring global flow of funds: who-to-whom matrix and financial network
This study improves upon global flow of funds (GFF) statistics to measure global financial stability at the national and cross-border sectoral...
-
Modeling Handwritten Digits Dataset Using the Matrix Variate t Distribution
In this paper, we consider matrix variate t distribution and explore some of its distributional properties to model handwritten digits dataset. In...
-
A Network Analysis of the Sectoral From-Whom-To-Whom Financial Stock Matrix
This study enhances global flow of funds (GFF) statistics for assessing global financial stability at the national and cross-border sectoral levels....
-
Matrix-variate Smooth Transition Models for Temporal Networks
In many fields, network analysis is used to investigate complex relationships. The increased availability of temporal network data opens the way to...
-
Elementary Matrix Operations
The mathematics for studying the properties of matrices is called matrix algebra or linear algebra. This first chapter treats the introductory part...