id: 06487941
dt: b
an: 2016b.00653
au: Saff, Edward Barry; Snider, Arthur David
ti: Fundamentals of matrix analysis with applications.
so: Hoboken, NJ: John Wiley \& Sons (ISBN 978-1-118-95365-5/hbk;
978-1-118-99541-9/set). xii, 395~p. (2016).
py: 2016
pu: Hoboken, NJ: John Wiley \& Sons
la: EN
cc: H65
ut:
ci:
li:
ab: Publisher’s description: Providing comprehensive coverage of matrix
theory from a geometric and physical perspective, the book describes
the functionality of matrices and their ability to quantify and analyze
many practical applications. Written by a highly qualified author team,
the book presents tools for matrix analysis and is illustrated with
extensive examples and software implementations. Beginning with a
detailed exposition and review of the Gauss elimination method, the
authors maintain readers’ interest with refreshing discussions
regarding the issues of operation counts, computer speed and precision,
complex arithmetic formulations, parameterization of solutions, and the
logical traps that dictate strict adherence to Gauss’s instructions.
The book heralds matrix formulation both as notational shorthand and as
a quantifier of physical operations such as rotations, projections,
reflections, and the Gauss reductions. Inverses and eigenvectors are
visualized first in an operator context before being addressed
computationally. Least squares theory is expounded in all its
manifestations including optimization, orthogonality, computational
accuracy, and even function theory. The book also features:{ indent=5mm
\item{‒} Novel approaches employed to explicate the QR, singular
value, Schur, and Jordan decompositions and their applications;
\item{‒} Coverage of the role of the matrix exponential in the
solution of linear systems of differential equations with constant
coefficients; \item{‒} Chapter-by-chapter summaries, review problems,
technical writing exercises, select solutions, and group projects to
aid comprehension of the presented concepts. } This is an excellent
textbook for undergraduate courses in linear algebra and matrix theory
for students majoring in mathematics, engineering, and science. The
book is also an accessible go-to reference for readers seeking
clarification of the fine points of kinematics, circuit theory, control
theory, computational statistics, and numerical algorithms.
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