Positive Definite Matrices (princeton Series In Applied Mathematics)
by Rajendra Bhatia /
2007 / English / PDF
1.7 MB Download
This book represents the first synthesis of the considerable body
of new research into positive definite matrices. These matrices
play the same role in noncommutative analysis as positive real
numbers do in classical analysis. They have theoretical and
computational uses across a broad spectrum of disciplines,
including calculus, electrical engineering, statistics, physics,
numerical analysis, quantum information theory, and geometry.
Through detailed explanations and an authoritative and inspiring
writing style, Rajendra Bhatia carefully develops general
techniques that have wide applications in the study of such
matrices.
This book represents the first synthesis of the considerable body
of new research into positive definite matrices. These matrices
play the same role in noncommutative analysis as positive real
numbers do in classical analysis. They have theoretical and
computational uses across a broad spectrum of disciplines,
including calculus, electrical engineering, statistics, physics,
numerical analysis, quantum information theory, and geometry.
Through detailed explanations and an authoritative and inspiring
writing style, Rajendra Bhatia carefully develops general
techniques that have wide applications in the study of such
matrices.
Bhatia introduces several key topics in functional analysis,
operator theory, harmonic analysis, and differential
geometry--all built around the central theme of positive definite
matrices. He discusses positive and completely positive linear
maps, and presents major theorems with simple and direct proofs.
He examines matrix means and their applications, and shows how to
use positive definite functions to derive operator inequalities
that he and others proved in recent years. He guides the reader
through the differential geometry of the manifold of positive
definite matrices, and explains recent work on the geometric mean
of several matrices.
Bhatia introduces several key topics in functional analysis,
operator theory, harmonic analysis, and differential
geometry--all built around the central theme of positive definite
matrices. He discusses positive and completely positive linear
maps, and presents major theorems with simple and direct proofs.
He examines matrix means and their applications, and shows how to
use positive definite functions to derive operator inequalities
that he and others proved in recent years. He guides the reader
through the differential geometry of the manifold of positive
definite matrices, and explains recent work on the geometric mean
of several matrices.Positive Definite Matrices
Positive Definite Matrices is an informative and useful
reference book for mathematicians and other researchers and
practitioners. The numerous exercises and notes at the end of
each chapter also make it the ideal textbook for graduate-level
courses.
is an informative and useful
reference book for mathematicians and other researchers and
practitioners. The numerous exercises and notes at the end of
each chapter also make it the ideal textbook for graduate-level
courses.