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A Thorough Guide to Elementary Matrix Algebra and Implementation in
R Basics of Matrix Algebra for Statistics with R provides a guide
to elementary matrix algebra sufficient for undertaking specialized
courses, such as multivariate data analysis and linear models. It
also covers advanced topics, such as generalized inverses of
singular and rectangular matrices and manipulation of partitioned
matrices, for those who want to delve deeper into the subject. The
book introduces the definition of a matrix and the basic rules of
addition, subtraction, multiplication, and inversion. Later topics
include determinants, calculation of eigenvectors and eigenvalues,
and differentiation of linear and quadratic forms with respect to
vectors. The text explores how these concepts arise in statistical
techniques, including principal component analysis, canonical
correlation analysis, and linear modeling. In addition to the
algebraic manipulation of matrices, the book presents numerical
examples that illustrate how to perform calculations by hand and
using R. Many theoretical and numerical exercises of varying levels
of difficulty aid readers in assessing their knowledge of the
material. Outline solutions at the back of the book enable readers
to verify the techniques required and obtain numerical answers.
Avoiding vector spaces and other advanced mathematics, this book
shows how to manipulate matrices and perform numerical calculations
in R. It prepares readers for higher-level and specialized studies
in statistics.
A Thorough Guide to Elementary Matrix Algebra and Implementation in
R Basics of Matrix Algebra for Statistics with R provides a guide
to elementary matrix algebra sufficient for undertaking specialized
courses, such as multivariate data analysis and linear models. It
also covers advanced topics, such as generalized inverses of
singular and rectangular matrices and manipulation of partitioned
matrices, for those who want to delve deeper into the subject. The
book introduces the definition of a matrix and the basic rules of
addition, subtraction, multiplication, and inversion. Later topics
include determinants, calculation of eigenvectors and eigenvalues,
and differentiation of linear and quadratic forms with respect to
vectors. The text explores how these concepts arise in statistical
techniques, including principal component analysis, canonical
correlation analysis, and linear modeling. In addition to the
algebraic manipulation of matrices, the book presents numerical
examples that illustrate how to perform calculations by hand and
using R. Many theoretical and numerical exercises of varying levels
of difficulty aid readers in assessing their knowledge of the
material. Outline solutions at the back of the book enable readers
to verify the techniques required and obtain numerical answers.
Avoiding vector spaces and other advanced mathematics, this book
shows how to manipulate matrices and perform numerical calculations
in R. It prepares readers for higher-level and specialized studies
in statistics.
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