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008			210717s2022 enk b 001 0 eng
010			_a 2021029851
020			_a9788195782901 _q(paperback)
040			_aLBSOR/DLC _beng _erda _cIISERB
042			_apcc
050	0	0	_aQA188 _b.K45 2022
082	0	0	_a512.9434 K527M _223
100	1		_aKhare, Apoorva. _929217
245	1	0	_aMatrix analysis and entrywise positivity preservers _cApoorva Khare.
260			_aNew Delhi: _bHindustan Book Agency, _c2022.
263			_a2112
300			_axxii, 339p.
504			_aIncludes bibliographical references and index.
505	0		_aThe cone of positive semidefinite matrices -- The Schur product theorem and nonzero lower bounds -- Totally positive (T P) and Totally non-negative (T N) matrices -- T P matrices--generalized Vandermonde and Hankel moment matrices -- Entrywise powers preserving positivity in fixed dimension -- Mid-convex implies continuous, and 2 x 2 preservers -- Entrywise preservers of positivity on matrices with zero patterns -- Entrywise powers preserving positivity, monotonicity, superadditivity -- Loewner convexity and single matrix encoders of preservers -- Exercises -- History--Schoenberg, Rudin, Vasudeva, and metric geometry -- Loewner's determinant calculation in Horn's thesis -- The stronger Horn-Loewner theorem, via mollifiers -- Stronger Vasudeva and Schoenberg theorems, via Bernstein's theorem -- Proof of stronger Schoenberg theorem (part I)--positivity certificates -- Proof of stronger Schoenberg theorem (part II)--real analyticity -- Proof of stronger Schoenberg theorem (part III)--complex analysis -- Preservers of Loewner positivity on kernels -- Preservers of Loewner monotonicity and convexity on kernels -- Functions acting outside forbidden diagonal blocks -- The Boas-Widder theorem on functions with positive differences -- Menger's results and Euclidean distance geometry -- Exercises -- Entrywise polynomial preservers and Horn-Loewner type conditions -- Polynomial preservers for rank-one matrices, via Schur polynomials -- First-order approximation and leading term of Schur polynomials -- Exact quantitative bound--monotonicity of Schur ratios -- Polynomial preservers on matrices with real or complex entries -- Cauchy and Littlewood's definitions of Schur polynomials -- Exercises.
650		0	_aMatrices. _929218
650		0	_aComposition operators. _929219
650		0	_aPositive operators. _929220
650		0	_aKernel functions. _929221
776	0	8	_iOnline version: _aKhare, Apoorva. _tMatrix analysis and entrywise positivity preservers _dCambridge, United Kingdom ; New York, NY : Cambridge University Press, 2022 _z9781108867122 _w(DLC) 2021029852
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
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999			_c10012 _d10012