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This is a book for the second course in linear algebra whereby
students are assumed to be familiar with calculations using real
matrices. To facilitate a smooth transition into rigorous proofs,
it combines abstract theory with matrix calculations.This book
presents numerous examples and proofs of particular cases of
important results before the general versions are formulated and
proved. The knowledge gained from a particular case, that
encapsulates the main idea of a general theorem, can be easily
extended to prove another particular case or a general case. For
some theorems, there are two or even three proofs provided. In this
way, students stand to gain and study important results from
different angles and, at the same time, see connections between
different results presented in the book.
The book is an introduction to linear algebra intended as a
textbook for the first course in linear algebra. In the first six
chapters we present the core topics: matrices, the vector space n,
orthogonality in n, determinants, eigenvalues and eigenvectors, and
linear transformations. The book gives students an opportunity to
better understand linear algebra in the next three chapters: Jordan
forms by examples, singular value decomposition, and quadratic
forms and positive definite matrices.In the first nine chapters
everything is formulated in terms of n. This makes the ideas of
linear algebra easier to understand. The general vector spaces are
introduced in Chapter 10. The last chapter presents problems solved
with a computer algebra system. At the end of the book we have
results or solutions for odd numbered exercises.
'The last section is an interesting collection of geometry problems
and their solutions from various International Mathematics Olympics
... There are a sufficient number of exercises at the end of each
chapter, and the answers to half of them are included at the end of
the book, with an occasional full solution here and there. The book
prepares the reader for a traditional introductory textbook in
linear algebra.'CHOICEThe book makes a first course in linear
algebra more accessible to the majority of students and it assumes
no prior knowledge of the subject. It provides a careful
presentation of particular cases of all core topics. Students will
find that the explanations are clear and detailed in manner. It is
considered as a bridge over the obstacles in linear algebra and can
be used with or without the help of an instructor.While many linear
algebra texts neglect geometry, this book includes numerous
geometrical applications. For example, the book presents classical
analytic geometry using concepts and methods from linear algebra,
discusses rotations from a geometric viewpoint, gives a rigorous
interpretation of the right-hand rule for the cross product using
rotations and applies linear algebra to solve some nontrivial plane
geometry problems.Many students studying mathematics, physics,
engineering and economics find learning introductory linear algebra
difficult as it has high elements of abstraction that are not easy
to grasp. This book will come in handy to facilitate the
understanding of linear algebra whereby it gives a comprehensive,
concrete treatment of linear algebra in R(2) and R(3). This method
has been shown to improve, sometimes dramatically, a student's view
of the subject.
'The last section is an interesting collection of geometry problems
and their solutions from various International Mathematics Olympics
... There are a sufficient number of exercises at the end of each
chapter, and the answers to half of them are included at the end of
the book, with an occasional full solution here and there. The book
prepares the reader for a traditional introductory textbook in
linear algebra.'CHOICEThe book makes a first course in linear
algebra more accessible to the majority of students and it assumes
no prior knowledge of the subject. It provides a careful
presentation of particular cases of all core topics. Students will
find that the explanations are clear and detailed in manner. It is
considered as a bridge over the obstacles in linear algebra and can
be used with or without the help of an instructor.While many linear
algebra texts neglect geometry, this book includes numerous
geometrical applications. For example, the book presents classical
analytic geometry using concepts and methods from linear algebra,
discusses rotations from a geometric viewpoint, gives a rigorous
interpretation of the right-hand rule for the cross product using
rotations and applies linear algebra to solve some nontrivial plane
geometry problems.Many students studying mathematics, physics,
engineering and economics find learning introductory linear algebra
difficult as it has high elements of abstraction that are not easy
to grasp. This book will come in handy to facilitate the
understanding of linear algebra whereby it gives a comprehensive,
concrete treatment of linear algebra in R(2) and R(3). This method
has been shown to improve, sometimes dramatically, a student's view
of the subject.
The book is an introduction to linear algebra intended as a
textbook for the first course in linear algebra. In the first six
chapters we present the core topics: matrices, the vector space n,
orthogonality in n, determinants, eigenvalues and eigenvectors, and
linear transformations. The book gives students an opportunity to
better understand linear algebra in the next three chapters: Jordan
forms by examples, singular value decomposition, and quadratic
forms and positive definite matrices.In the first nine chapters
everything is formulated in terms of n. This makes the ideas of
linear algebra easier to understand. The general vector spaces are
introduced in Chapter 10. The last chapter presents problems solved
with a computer algebra system. At the end of the book we have
results or solutions for odd numbered exercises.
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