000			01848nam a22002177a 4500
003			OSt
005			20241001112748.0
008			200318b ||||| |||| 00| 0 eng d
020			_a9789380250038
040			_cEducational Supplies _aICTS-TIFR
050			_aQA188.BHA
100			_aRajendra Bhatia
245			_aPositive definite matrices
260			_aNew Delhi: _bHindustan Book Agency, _c[c2007]
300			_a251 p
490			_aTexts and Readings in Mathematics _v44
505			_a1. Positive Matrices 2. Positive Linear Maps 3. Completely Positive Maps 4. Matrix Means 5. Positive Definite Functions 6. Geometry of Positive Matrices
520			_aTRIM 44This 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. The author 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. --- summary provided by publisher
650			_aMathematics
942			_2lcc _cBK
999			_c3057 _d3057