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Undergraduate-level introduction to linear algebra and matrix
theory deals with matrices and linear systems, vector spaces,
determinants, linear transformations, similarity, polynomials,
and polynomial matrices. Also spectral decomposition, Jordan
canonical form, solution of the matrix equation AX=XB, and over
375 problems, many with answers. "Comprehensive." —
Electronic Engineer's Design Magazine.

Differential algebraic equations (DAEs), including so-called
descriptor systems, began to attract significant research interest
in applied and numerical mathematics in the early 1980s, no more
than about three decades ago. In this relatively short time, DAEs
have become a widely acknowledged tool to model processes subjected
to constraints, in order to simulate and to control processes
in various application fields such as network simulation,... more...

This book presents advances in matrix and tensor data processing in
the domain of signal, image and information processing. The
theoretical mathematical approaches are discusses in the context of
potential applications in sensor and cognitive systems engineering.
The topics and application include Information Geometry,
Differential Geometry of structured Matrix, Positive Definite
Matrix, Covariance Matrix, Sensors (Electromagnetic Fields,
Acoustic... more...

This monograph is concerned with the fitting of linear
relationships in the context of the linear statistical model. As
alternatives to the familiar least squared residuals procedure, it
investigates the relationships between the least absolute
residuals, the minimax absolute residual and the least median of
squared residuals procedures. It is intended for graduate students
and research workers in statistics with some command of matrix
analysis and... more...

Classical valuation theory has applications in number theory and
class field theory as well as in algebraic geometry, e.g. in a
divisor theory for curves. But the noncommutative equivalent
is mainly applied to finite dimensional skewfields. Recently
however, new types of algebras have become popular in modern
algebra; Weyl algebras, deformed and quantized algebras, quantum
groups and Hopf algebras, etc. The advantage of valuation theory in... more...

The Jacobian of a smooth projective curve is undoubtedly one of the
most remarkable and beautiful objects in algebraic geometry. This
work is an attempt to develop an analogous theory for smooth
projective surfaces - a theory of the nonabelian Jacobian of smooth
projective surfaces. Just like its classical counterpart, our
nonabelian Jacobian relates to vector bundles (of rank 2) on a
surface as well as its Hilbert scheme of points. But it also comes... more...

The author defines “Geometric Algebra Computing” as the
geometrically intuitive development of algorithms using geometric
algebra with a focus on their efficient implementation, and the
goal of this book is to lay the foundations for the widespread use
of geometric algebra as a powerful, intuitive mathematical language
for engineering applications in academia and industry. The related
technology is driven by the invention of conformal geometric... more...

The goal of this book is to describe the most powerful methods for
evaluating multiloop Feynman integrals that are currently used in
practice. This book supersedes the author’s previous Springer
book “Evaluating Feynman Integrals” and its textbook version
“Feynman Integral Calculus.” Since the publication of these two
books, powerful new methods have arisen and conventional methods
have been improved on in essential ways. A further... more...

This monograph provides an introduction to the theory of Clifford
algebras, with an emphasis on its connections with the theory of
Lie groups and Lie algebras. The book starts with a detailed
presentation of the main results on symmetric bilinear forms and
Clifford algebras. It develops the spin groups and the spin
representation, culminating in Cartan’s famous triality
automorphism for the group Spin(8). The discussion of enveloping
algebras... more...

The present manuscript is an improved edition of a text that first
appeared under the same title in Bonner Mathematische Schriften,
no.26, and originated from a series of lectures given by the author
in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to
provide the reader, acquainted with the basics of algebraic number
theory, a quick and immediate access to class field theory. This
script consists of three parts, the first of which... more...