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The Less Is More Linear Algebra of Vector Spaces and Matrices (Paperback)
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The Less Is More Linear Algebra of Vector Spaces and Matrices (Paperback)
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Designed for a proof-based course on linear algebra, this rigorous
and concise textbook intentionally introduces vector spaces, inner
products, and vector and matrix norms before Gaussian elimination
and eigenvalues so students can quickly discover the singular value
decomposition (SVD)-arguably the most enlightening and useful of
all matrix factorizations. Gaussian elimination is then introduced
after the SVD and the four fundamental subspaces and is presented
in the context of vector spaces rather than as a computational
recipe. This allows the authors to use linear independence,
spanning sets and bases, and the four fundamental subspaces to
explain and exploit Gaussian elimination and the LU factorization,
as well as the solution of overdetermined linear systems in the
least squares sense and eigenvalues and eigenvectors. This unique
textbook also includes examples and problems focused on concepts
rather than the mechanics of linear algebra. The problems at the
end of each chapter and in an associated website encourage readers
to explore how to use the notions introduced in the chapter in a
variety of ways. Additional problems, quizzes, and exams will be
posted on an accompanying website and updated regularly. The Less
Is More Linear Algebra of Vector Spaces and Matrices is for
students and researchers interested in learning linear algebra who
have the mathematical maturity to appreciate abstract concepts that
generalize intuitive ideas. The early introduction of the SVD makes
the book particularly useful for those interested in using linear
algebra in applications such as scientific computing and data
science. It is appropriate for a first proof-based course in linear
algebra.
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