LEADER 05478nam 2200673Ia 450 001 9911020350103321 005 20200520144314.0 010 $a9786613306234 010 $a9781283306232 010 $a1283306239 010 $a9781118032893 010 $a1118032896 010 $a9781118031148 010 $a1118031148 035 $a(CKB)2550000000056883 035 $a(EBL)694976 035 $a(SSID)ssj0000555255 035 $a(PQKBManifestationID)11359230 035 $a(PQKBTitleCode)TC0000555255 035 $a(PQKBWorkID)10518762 035 $a(PQKB)11060998 035 $a(MiAaPQ)EBC694976 035 $a(OCoLC)761321479 035 $a(Perlego)2772663 035 $a(EXLCZ)992550000000056883 100 $a19980724d1999 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aOrthogonal sets and polar methods in linear algebra $eapplications to matrix calculations, systems of equations, inequalities, and linear programming /$fEnrique Castillo ... [et al.] 210 $aNew York $cWiley$dc1999 215 $a1 online resource (440 p.) 225 1 $aPure and applied mathematics 300 $aDescription based upon print version of record. 311 08$a9780471328896 311 08$a0471328898 320 $aIncludes bibliographical references (p. 415-418) and index. 327 $aOrthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear Programming; Contents; Part I Linear Spaces and Systems of Equations; 1 Basic Concepts; 1.1 Introduction; 1.2 Linear space; 1.3 The Euclidean Space En; 1.4 Orthogonal Sets and Decompositions; 1.5 Matrices; 1.6 Systems of Linear Equations; Exercises; 2 Orthogonal Sets; 2.1 Introduction and Motivation; 2.2 Orthogonal Decompositions; 2.3 The Orthogonalization Module; 2.4 Mathematica Program; Exercises; 3 Matrix Calculations Using Orthogonal Sets 327 $a3.1 Introduction3.2 Inverting a Matrix; 3.3 The Rank of a Matrix; 3.4 Calculating the Determinant of a Matrix; 3.5 Algorithm for Matrix Calculations; 3.6 Complexity; 3.7 Inverses and Determinants of Row-Modified Matrices; 3.8 Inverses of Symbolic Matrices; 3.9 Extensions to Partitioned Matrices; 3.10 Inverses of Modified Matrices; 3.11 Mathematica Programs; Exercises; 4 More Applications of Orthogonal Sets; 4.1 Intersection of Two Linear Subspaces; 4.2 Reciprocals Images in Linear Transformations; 4.3 Other Applications; 4.4 Mathematica Programs; Exercises 327 $a5 Orthogonal Sets and Systems of Linear Equations5.1 Introduction; 5.2 Compatibility of a System of Linear Equations; 5.3 Solving a System of Linear Equations; 5.4 Complexity; 5.5 Checking Systems Equivalence; 5.6 Solving a System in Some Selected Variables; 5.7 Modifying Systems of Equations; 5.8 Applications; 5.9 Mathematica Programs; Exercises; Appendix: Proof of Lemma 5.2; Part II Cones and Systems of Inequalities; 6 Polyhedral Convex Cones; 6.1 Introduction; 6.2 Convex Sets; 6.3 Types of Linear Combinations; 6.4 Polyhedral Convex Cones; 6.5 The ? -Process; 6.6 The Complete ?-Algorithm 327 $a6.7 Mathematica ProgramExercises; 7 Polytopes and Polyhedra; 7.1 Introduction; 7.2 Polytopes; 7.3 Polyhedra; Exercises; 8 Cones and Systems of Inequalities; 8.1 Introduction; 8.2 A Discussion of Linear Systems; 8.3 Solving Linear Systems; 8.4 Applications to Linear Programming; Exercises; Part III Linear Programming; 9 An Introduction to Linear Programming; 9.1 Introduction; 9.2 Problem Statement and Basic Definitions; 9.3 Linear Programming Problem in Standard Form; 9.4 Basic Solutions; 9.5 Duality; Exercises; 10 The Exterior Point Method; 10.1 Introduction; 10.2 The Exterior Point Method 327 $a10.3 Making the EPM More Efficient10.4 Complexity; 10.5 Recovering the Final Tableau from the Solution; 10.6 Modifying a Linear Programming Problem; Exercises; Part IV Applications; 11 Applications; 11.1 Introduction; 11.2 Matrix Analysis of Engineering Structures; 11.3 The Transportation Problem; 11.4 Production-Scheduling Problems; 11.5 The Input-Output Tables; 11.6 The Diet Problem; 11.7 Network Flow Problems; Exercises; Part V Appendices; Appendix A: A Java Application; A.l How to Use the Program; Appendix B: List of Notation; References; Index 330 $aA unique, applied approach to problem solving in linear algebraDeparting from the standard methods of analysis, this unique book presents methodologies and algorithms based on the concept of orthogonality and demonstrates their application to both standard and novel problems in linear algebra. Covering basic theory of linear systems, linear inequalities, and linear programming, it focuses on elegant, computationally simple solutions to real-world physical, economic, and engineering problems. The authors clearly explain the reasons behind the analysis of different structures and concept 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aAlgebras, Linear 606 $aOrthogonalization methods 615 0$aAlgebras, Linear. 615 0$aOrthogonalization methods. 676 $a512.5 701 $aCastillo$b Enrique$f1946-$059628 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911020350103321 996 $aOrthogonal sets and polar methods in linear algebra$94416651 997 $aUNINA