An accessible and clear introduction to linear algebra with a focus
on matrices and engineering applications Providing comprehensive
coverage of matrix theory from a geometric and physical
perspective, Fundamentals of Matrix Analysis with Applications
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. Fundamentals of Matrix Analysis
with Applications also features: * Novel approaches employed to
explicate the QR, singular value, Schur, and Jordan decompositions
and their applications * Coverage of the role of the matrix
exponential in the solution of linear systems of differential
equations with constant coefficients * Chapter-by-chapter
summaries, review problems, technical writing exercises, select
solutions, and group projects to aid comprehension of the presented
concepts Fundamentals of Matrix Analysis with Applications 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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