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Books > Science & Mathematics > Mathematics > Algebra
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Advanced Topics in Linear Algebra - Weaving Matrix Problems through the Weyr Form (Hardcover)
Loot Price: R1,903
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Advanced Topics in Linear Algebra - Weaving Matrix Problems through the Weyr Form (Hardcover)
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Advanced Topics in Linear Algebra presents, in an engaging style,
novel topics linked through the Weyr matrix canonical form, a
largely unknown cousin of the Jordan canonical form discovered by
Eduard Weyr in 1885. The book also develops much linear algebra
unconnected to canonical forms, that has not previously appeared in
book form. It presents common applications of Weyr form, including
matrix commutativity problems, approximate simultaneous
diagonalization, and algebraic geometry, with the latter two having
topical connections to phylogenetic invariants in biomathematics
and multivariate interpolation. The Weyr form clearly outperforms
the Jordan form in many situations, particularly where two or more
commuting matrices are involved, due to the block upper triangular
form a Weyr matrix forces on any commuting matrix. In this book,
the authors develop the Weyr form from scratch, and include an
algorithm for computing it. The Weyr form is also derived
ring-theoretically in an entirely different way to the classical
derivation of the Jordan form. A fascinating duality exists between
the two forms that allows one to flip back and forth and exploit
the combined powers of each. The book weaves together ideas from
various mathematical disciplines, demonstrating dramatically the
variety and unity of mathematics. Though the book's main focus is
linear algebra, it also draws upon ideas from commutative and
noncommutative ring theory, module theory, field theory, topology,
and algebraic geometry. Advanced Topics in Linear Algebra offers
self-contained accounts of the non-trivial results used from
outside linear algebra, and lots of worked examples, thereby making
it accessible to graduate students. Indeed, the scope of the book
makes it an appealing graduate text, either as a reference or for
an appropriately designed one or two semester course. A number of
the authors' previously unpublished results appear as well.
General
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