LEADER 04436nam 22005535 450 001 9910480581503321 005 20200704234407.0 010 $a1-4613-8498-2 024 7 $a10.1007/978-1-4613-8498-4 035 $a(CKB)3400000000093275 035 $a(SSID)ssj0000807671 035 $a(PQKBManifestationID)11417237 035 $a(PQKBTitleCode)TC0000807671 035 $a(PQKBWorkID)10756370 035 $a(PQKB)10146730 035 $a(DE-He213)978-1-4613-8498-4 035 $a(MiAaPQ)EBC3078865 035 $a(PPN)238056694 035 $a(EXLCZ)993400000000093275 100 $a20121227d1997 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNumerical Range$b[electronic resource] $eThe Field of Values of Linear Operators and Matrices /$fby Karl E. Gustafson, Duggirala K.M. Rao 205 $a1st ed. 1997. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1997. 215 $a1 online resource (XIV, 190 p. 11 illus. in color.) 225 1 $aUniversitext,$x0172-5939 300 $a"With 9 figues." 311 $a0-387-94835-X 320 $aIncludes bibliographical references and index. 327 $a1 Numerical Range -- 1.1 Elliptic Range -- 1.2 Spectral Inclusion -- 1.3 Numerical Radius -- 1.4 Normal Operators -- 1.5 Numerical Boundary -- 1.6 Other W-Ranges -- Endnotes for Chapter 1 -- 2 Mapping Theorems -- 2.1 Radius Mapping -- 2.2 Analytic Functions -- 2.3 Rational Functions -- 2.4 Operator Products -- 2.5 Commuting Operators -- 2.6 Dilation Theory -- Endnotes for Chapter 2 -- 3 Operator Trigonometry -- 3.1 Operator Angles -- 3.2 Minmax Equality -- 3.3 Operator Deviations -- 3.4 Semigroup Generators -- 3.5 Accretive Products -- 3.6 Antieigenvalue Theory -- Endnotes for Chapter 3 -- 4 Numerical Analysis -- 4.1 Optimization Algorithms -- 4.2 Conjugate Gradient -- 4.3 Discrete Stability -- 4.4 Fluid Dynamics -- 4.5 Lax?Wendroff Scheme -- 4.6 Pseudo Eigenvalues -- Endnotes for Chapter 4 -- 5 Finite Dimensions -- 5.1 Value Field -- 5.2 Gersgorin Sets -- 5.3 Radius Estimates -- 5.4 Hadamard Product -- 5.5 Generalized Ranges -- 5.6 W(A) Computation -- Endnotes for Chapter 5 -- 6 Operator Classes -- 6.1 Resolvent Growth -- 6.2 Three Classes -- 6.3 Spectral Sets -- 6.4 Normality Conditions -- 6.5 Finite Inclusions -- 6.6 Beyond Spectraloid -- Endnotes for Chapter 6. 330 $aThe theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen­ sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func­ tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu­ nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region. 410 0$aUniversitext,$x0172-5939 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aAnalysis. 676 $a515/.7246 700 $aGustafson$b Karl E$4aut$4http://id.loc.gov/vocabulary/relators/aut$059420 702 $aRao$b Duggirala K.M$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910480581503321 996 $aNumerical range$9375298 997 $aUNINA