Totally Nonnegative Matrices
Apr 2011 · Princeton University Press
eBook
264
Halaman
family_home
Memenuhi syarat
info
reportRating dan ulasan tidak diverifikasi Pelajari Lebih Lanjut
Tentang eBook ini
Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics.
The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references.
The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references.
Tentang pengarang
Shaun M. Fallat is professor of mathematics and statistics at the University of Regina. Charles R. Johnson is the Class of 1961 Professor of Mathematics at the College of William & Mary.
Beri rating eBook ini
Sampaikan pendapat Anda.
Informasi bacaan
Smartphone dan tablet
Instal aplikasi Google Play Buku untuk Android dan iPad/iPhone. Aplikasi akan disinkronkan secara otomatis dengan akun Anda dan dapat diakses secara online maupun offline di mana saja.
Laptop dan komputer
Anda dapat mendengarkan buku audio yang dibeli di Google Play menggunakan browser web komputer.
eReader dan perangkat lainnya
Untuk membaca di perangkat e-ink seperti Kobo eReaders, Anda perlu mendownload file dan mentransfernya ke perangkat Anda. Ikuti petunjuk Pusat bantuan yang mendetail untuk mentransfer file ke eReaders yang didukung.
