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This book provides a self-contained and accessible introduction to
linear and multilinear algebra. Besides the standard techniques for
linear and multilinear algebra many advanced topics are included.
Emphasis is placed on the Kronecker product and tensor product. The
Kronecker product has widespread applications in signal processing,
discrete wavelets, statistical physics, computer graphics,
fractals, quantum mechanics and quantum computing. All these fields
are covered in detail. A key feature of the book is the many
detailed worked-out examples. Computer algebra applications are
also given. Each chapter includes useful exercises. The book is
well suited for pure and applied mathematicians as well as
theoretical physicists and engineers.
New topics added to the second edition are: braid-like
relations, Clebsch Gordan expansion, nearest Kronecker product,
Clifford and Pauli group, universal enveloping algebra, computer
algebra and Kronecker product.
Our self-contained volume provides an accessible introduction to
linear and multilinear algebra as well as tensor calculus. Besides
the standard techniques for linear algebra, multilinear algebra and
tensor calculus, many advanced topics are included where emphasis
is placed on the Kronecker product and tensor product. The
Kronecker product has widespread applications in signal processing,
discrete wavelets, statistical physics, Hopf algebra, Yang-Baxter
relations, computer graphics, fractals, quantum mechanics, quantum
computing, entanglement, teleportation and partial trace. All these
fields are covered comprehensively.The volume contains many
detailed worked-out examples. Each chapter includes useful
exercises and supplementary problems. In the last chapter, software
implementations are provided for different concepts. The volume is
well suited for pure and applied mathematicians as well as
theoretical physicists and engineers.New topics added to the third
edition are: mutually unbiased bases, Cayley transform, spectral
theorem, nonnormal matrices, Gateaux derivatives and matrices,
trace and partial trace, spin coherent states, Clebsch-Gordan
series, entanglement, hyperdeterminant, tensor eigenvalue problem,
Carleman matrix and Bell matrix, tensor fields and Ricci tensors,
and software implementations.
'This is a very useful book which helps to understand the concepts
of quantum computing and quantum information by well presented
problems and detailed solutions ... It is highly recommended for
beginners as well as for advanced researchers.'zbMATHQuantum
computing and quantum information are two of the fastest growing
and most exciting research fields in physics. Entanglement,
teleportation and the possibility of using the non-local behavior
of quantum mechanics to factor integers in random polynomial time
have also added to this new interest.This book presents a huge
collection of problems in quantum computing and quantum information
together with their detailed solutions, which will prove to be
invaluable to students as well as researchers in these fields. Each
chapter gives a comprehensive introduction to the topics. All the
important concepts and areas such as quantum gates and quantum
circuits, product Hilbert spaces, entanglement and entanglement
measures, teleportation, Bell states, Bell measurement, Bell
inequality, Schmidt decomposition, quantum Fourier transform, magic
gate, von Neumann entropy, quantum cryptography, quantum error
corrections, quantum games, number states and Bose operators,
coherent states, squeezed states, Gaussian states, coherent Bell
states, POVM measurement, quantum optics networks, beam splitter,
phase shifter and Kerr Hamilton operator are included. A chapter on
quantum channels has also been added. Furthermore a chapter on
boolean functions and quantum gates with mapping bits to qubits is
included.The topics range in difficulty from elementary to
advanced. Almost all problems are solved in detail and most of the
problems are self-contained. Each chapter also contains
supplementary problems to challenge the reader. Programming
problems with Maxima and SymbolicC++ implementations are also
provided.
'This is a very useful book which helps to understand the concepts
of quantum computing and quantum information by well presented
problems and detailed solutions ... It is highly recommended for
beginners as well as for advanced researchers.'zbMATHQuantum
computing and quantum information are two of the fastest growing
and most exciting research fields in physics. Entanglement,
teleportation and the possibility of using the non-local behavior
of quantum mechanics to factor integers in random polynomial time
have also added to this new interest.This book presents a huge
collection of problems in quantum computing and quantum information
together with their detailed solutions, which will prove to be
invaluable to students as well as researchers in these fields. Each
chapter gives a comprehensive introduction to the topics. All the
important concepts and areas such as quantum gates and quantum
circuits, product Hilbert spaces, entanglement and entanglement
measures, teleportation, Bell states, Bell measurement, Bell
inequality, Schmidt decomposition, quantum Fourier transform, magic
gate, von Neumann entropy, quantum cryptography, quantum error
corrections, quantum games, number states and Bose operators,
coherent states, squeezed states, Gaussian states, coherent Bell
states, POVM measurement, quantum optics networks, beam splitter,
phase shifter and Kerr Hamilton operator are included. A chapter on
quantum channels has also been added. Furthermore a chapter on
boolean functions and quantum gates with mapping bits to qubits is
included.The topics range in difficulty from elementary to
advanced. Almost all problems are solved in detail and most of the
problems are self-contained. Each chapter also contains
supplementary problems to challenge the reader. Programming
problems with Maxima and SymbolicC++ implementations are also
provided.
This book provides an extensive collection of problems with
detailed solutions in introductory and advanced matrix calculus.
Supplementary problems in each chapter will challenge and excite
the reader, ideal for both graduate and undergraduate mathematics
and theoretical physics students. The coverage includes systems of
linear equations, linear differential equations, integration and
matrices, Kronecker product and vec-operation as well as functions
of matrices. Furthermore, specialized topics such as spectral
theorem, nonnormal matrices and mutually unbiased bases are
included. Many of the problems are related to applications for
group theory, Lie algebra theory, wavelets, graph theory and
matrix-valued differential forms, benefitting physics and
engineering students and researchers alike. It also branches out to
problems with tensors and the hyperdeterminant. Computer algebra
programs in Maxima and SymbolicC++ have also been provided.
This book provides an extensive collection of problems with
detailed solutions in introductory and advanced matrix calculus.
Supplementary problems in each chapter will challenge and excite
the reader, ideal for both graduate and undergraduate mathematics
and theoretical physics students. The coverage includes systems of
linear equations, linear differential equations, integration and
matrices, Kronecker product and vec-operation as well as functions
of matrices. Furthermore, specialized topics such as spectral
theorem, nonnormal matrices and mutually unbiased bases are
included. Many of the problems are related to applications for
group theory, Lie algebra theory, wavelets, graph theory and
matrix-valued differential forms, benefitting physics and
engineering students and researchers alike. It also branches out to
problems with tensors and the hyperdeterminant. Computer algebra
programs in Maxima and SymbolicC++ have also been provided.
This book provides a comprehensive collection of problems together
with their detailed solutions for Bose, Spin, Fermi systems and
also interacting systems. Supplementary problems are also provided.
Exercises for representations of Lie groups and Lie algebras are
also covered as well as computer algebra implementations. It is the
only book which summarizes these topics from the quantum theory
aspect in the form of exercises and solutions. The book is also
self-contained.Both physicists and mathematicians will benefit from
all the different techniques explained and worked out in detail.
Quantum computing and quantum information are two of the fastest
growing and most exciting research fields in physics. Entanglement,
teleportation and the possibility of using the non-local behavior
of quantum mechanics to factor integers in random polynomial time
have also added to this new interest. This book supplies a huge
collection of problems in quantum computing and quantum information
together with their detailed solutions, which will prove to be
invaluable to students as well as researchers in these fields. All
the important concepts and topics such as quantum gates and quantum
circuits, product Hilbert spaces, entanglement and entanglement
measures, deportation, Bell states, Bell inequality, Schmidt
decomposition, quantum Fourier transform, magic gate, von Neumann
entropy, quantum cryptography, quantum error corrections, number
states and Bose operators, coherent states, squeezed states,
Gaussian states, POVM measurement, quantum optics networks, beam
splitter, phase shifter and Kerr Hamilton operator are included.
The topics range in difficulty from elementary to advanced. Almost
all problems are solved in detail and most of the problems are
self-contained.
Solving problems in quantum mechanics is an essential skill and
research activity for physicists, mathematicians, engineers and
others. Nowadays, the labor of scientific computation has been
greatly eased by the advent of computer algebra packages, which do
not merely perform number crunching, but also enable users to
manipulate algebraic expressions and equations symbolically. For
example, the manipulations of noncommutative operators,
differentiation and integration can now be carried out
algebraically by the computer algebra package.This book collects
standard and advanced methods in quantum mechanics and implements
them using SymbolicC++ and Maxima, two popular computer algebra
packages. Throughout, the sample programs and their outputs are
accompanied with explanatory text of the underlying mathematics and
physics explained in detail. Selected problems have also been
implemented using two other popular packages - Mathematica and
Maple - while some problems are implemented in C++.Modern
developments in quantum theory are covered extensively, beyond the
standard quantum mechanical techniques. The new research topics
added to this second edition are: entanglement, teleportation,
Berry phase, Morse oscillator, Magnus expansion, wavelets, Pauli
and Clifford groups, coupled Bose-Fermi systems, super-Lie
algebras, etc.
The book presents examples of important techniques and theorems for
Groups, Lie groups and Lie algebras. This allows the reader to gain
understandings and insights through practice. Applications of these
topics in physics and engineering are also provided. The book is
self-contained. Each chapter gives an introduction to the topic.
Symbolic C++: An Introduction to Computer Algebra Using Object-Oriented Programming provides a concise introduction to C++ and object-oriented programming, using a step-by-step construction of a new object-oriented designed computer algebra system - Symbolic C++. It shows how object-oriented programming can be used to implement a symbolic algebra system and how this can then be applied to different areas in mathematics and physics. This second revised edition:- * Explains the new powerful classes that have been added to Symbolic C++. * Includes the Standard Template Library. * Extends the Java section. * Contains useful classes in scientific computation. * Contains extended coverage of Maple, Mathematica, Reduce and MuPAD.
"Classical and Quantum computing" provides a self-contained,
systematic and comprehensive introduction to all the subjects and
techniques important in scientific computing. The style and
presentation are readily accessible to undergraduates and
graduates. A large number of examples, accompanied by complete C++
and Java code wherever possible, cover every topic.
Features and benefits:
- Comprehensive coverage of the theory with many examples
- Topics in classical computing include boolean algebra, gates,
circuits, latches, error detection and correction, neural networks,
Turing machines, cryptography, genetic algorithms
- For the first time, genetic expression programming is presented
in a textbook
- Topics in quantum computing include mathematical foundations,
quantum algorithms, quantum information theory, hardware used in
quantum computing
This book serves as a textbook for courses in scientific computing
and is also very suitable for self-study. Students, professionals
and practitioners in computer science, applied mathematics and
physics will benefit from using the book and the included software
simulations.
Scientific computing is a collection of tools, techniques and
theories required to develop and solve mathematical models in
science and engineering on a computer. This timely book provides
the various skills and techniques needed in scientific computing.
The topics range in difficulty from elementary to advanced, and all
the latest fields in scientific computing are covered such as
matrices, numerical analysis, neural networks, genetic algorithms,
etc. Presented in the format of problems and detailed solutions,
important concepts and techniques are introduced and developed.
Many problems include software simulations. Algorithms have
detailed implementations in C++ or Java. This book will prove to be
invaluable not only to students and research workers in the fields
of scientific computing, but also to teachers of this subject who
will find this text useful as a supplement. The topics discussed in
this book are part of the e-learning and distance learning courses
conducted by the International School of Scientific Computing,
South Africa.
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