Problems and Solutions in Introductory and Advanced Matrix Calculus

Problems and Solutions Contents

• Basic Operations
• Linear Equations 
• Kronecker Product
• Traces, Determinants, and Hyperdeterminants
• Eigenvalues and Eigenvectors 
• Spectral Theorem 
• Commutators and Anticommutators 
• Decomposition of Matrices
• Functions of Matrices
• Cayley-Hamilton Theorem 
• Hadamard Product 
• Norms and Scalar Products 
• vec Operator 
• Nonnormal Matrices 
• Binary Matrices 
• Star Product 
• Unitary Matrices 
• Groups, Lie Groups and Matrices 
•  Lie Algebras and Matrices 
• Braid Group
• Graphs and Matrices 
• Hilbert Spaces and Mutually Unbiased Bases 
• Linear Differential Equations 
• Differentiation and Matrices 
•  Integration and Matrices

Preface tp Problems and Solutions in Introductory and Advanced Matrix Calculus

The purpose of this book is to supply a collection of
problems in introductory and advanced matrix problems together with their
detailed solutions which will prove to be valuable to undergraduate and
graduate students as well as to research workers in these fields.

Each chapter
contains an introduction with the essential definitions and explanations to
tackle the problems in the chapter. If necessary, other concepts are explained
directly with the present problems. Thus the material in the book is
self-contained.

The topics range in difficulty from elementary to advanced.
Students can learn important principles and strategies required for problem-solving.

Lecturers will also find this text useful either as a supplement or
text since important concepts and techniques are developed in the problems.

A large number of problems are related to applications. Applications include
wavelets, linear integral equations, Kirchhoff’s laws, global positioning
systems, Floquet theory, octonions, random walks, entanglement, tensor
decomposition, hyperdeterminant, matrix-valued differential forms, Kronecker
product, and images.

A number of problems useful in quantum physics and graph
theory are also provided. Advanced topics include groups and matrices, Lie
groups and matrices, and Lie algebras and matrices. Exercises for matrix-valued
differential forms are also included.

In this second edition, new problems for
braid groups, mutually unbiased bases, vec operator, spectral theorem, binary
matrices, nonnormal matrices, wavelets, fractals, matrices, and integration are
added. Each chapter also contains supplementary problems.

Furthermore, a number
of Maxima and SymbolicC++ programs are added for solving problems. Applications
in mathematical and theoretical physics are emphasized.

The book can also be
used as a text for linear and multilinear algebra or matrix theory. The
material was tested in the first author’s lectures given around the world.

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Author(s): Hardy, Yorick; Steeb, Willi-Hans

Publisher: World Scientific Publishing Company, Year: 2017

ISBN: 9789813143784,9813143789

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