LEADER 05082nam 22006853u 450 001 9911006800003321 005 20230802010944.0 010 $a0-486-13504-7 010 $a1-62198-583-0 035 $a(CKB)2550000001186820 035 $a(EBL)1894763 035 $a(SSID)ssj0001002748 035 $a(PQKBManifestationID)12338862 035 $a(PQKBTitleCode)TC0001002748 035 $a(PQKBWorkID)11015959 035 $a(PQKB)11156359 035 $a(MiAaPQ)EBC1894763 035 $a(Au-PeEL)EBL1894763 035 $a(CaONFJC)MIL566191 035 $a(OCoLC)868273744 035 $a(EXLCZ)992550000001186820 100 $a20141222d2012|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLinear Algebra 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2012 215 $a1 online resource (670 p.) 225 1 $aDover Books on Mathematics 300 $aDescription based upon print version of record. 311 08$a0-486-63518-X 311 08$a1-306-34940-0 327 $aDOVER BOOKS ON MATHEMATICS; Title Page; Copyright Page; PREFACE; Table of Contents; chapter I - DETERMINANTS; I.I. Number Fields; I.2. Problems of the Theory of Systems of Linear Equations; I.3.Determinants of Order n; 1.4. Properties of Determinants; 1.5. Cofactors and Minors; 1.6. Practical Evaluation of Determinants; 1.7. Cramer's Rule; 1.8. Minors of Arbitrary Order. Laplace's Theorem; 1.9. Linear Dependence between Columns; chapter 2 - LINEAR SPACES; 2.1. Definitions; 2.2. Linear Dependence; 2.3 Bases, Components, Dimension; 2.4. Subspaces; 2.5. Linear Manifolds; 2.6. Hyperplanes 327 $a2.7. Morphisms of Linear Spaceschapter 3 - SYSTEMS OF LINEAR EQUATIONS; 3.1. More on the Rank of a Matrix; 3.2. Nontrivial Compatibility of a Homogeneous Linear System; 3.3. The Compatibility Condition for a General Linear System; 3.4. The General Solution of a Linear System; 3.5. Geometric Properties of the Solution Space; 3.6. Methods for Calculating the Rank of a Matrix; chapter 4 - LINEAR FUNCTIONS OF A VECTOR ARGUMENT; 4.1. Linear Forms; 4.2. Linear Operators; 4.3. Sums and Products of Operators; 4.4. Corresponding Operations on Matrices; 4.5. Further Properties of Matrix Multiplication 327 $a4.6.The Range and Null Space of a Linear Operator4.7. Linear Operators Mapping a Space Kn into Itself 2&; 4.8.Invariant Subspaces; 4.9.Eigenvectors and Eigenvalues; chapter 5 - COORDINATE TRANSFORMATIONS; 5.1. Transformation to a New Basis; 5.2. Consecutive Transformations; 5.3. Transformation of the Components of a Vector; 5.4. Transformation of the Coefficients of a Linear Form; 5.5. Transformation of the Matrix of a Linear Operator; *5.6. Tensors; chapter 6 - THE CANONICAL FORM OF THE MATRIX OF A LINEAR OPERATOR; 6.1 Canonical Form of the Matrix of a Nilpotent Operator . 327 $a6.2. Algebras. The Algebra of Polynomials6.3. Canonical Form of the Matrix of an Arbitrary Operator; 6.4. Elementary Divisors; 6.5. Further Implications; 6.6. The Real Jordan Canonical Form; *6.7. Spectra, Jets and Polynomials; *6.8. Operator Functions and Their Matrices; chapter 7 - BILINEAR AND QUADRATIC FORMS; 7.1. Bilinear Forms; 7.2. Quadratic Forms; 7.3. Reduction of a Quadratic Form to Canonical Form; 7.4. The Canonical Basis of a Bilinear Form; 7.5. Construction of a Canonical Basis by Jacobi's Method; 7.6. Adjoint Linear Operators 327 $a7.7. Isomorphism of Spaces Equipped with a Bilinear Form*7.8. Multilinear Forms; 7.9. Bilinear and Quadratic Forms in a Real Space; chapter 8 - EUCLIDEAN SPACES; 8.1. Introduction; 8.2. Definition of a Euclidean Space; 8.3. Basic Metric Concepts; 8.4. Orthogonal Bases; 8.5. Perpendiculars; 8.6. The Orthogonalization Theorem; 8.7. The Gram Determinant; 8.8. Incompatible Systems and the Method of Least Squares; 8.9. Adjoint Operators and Isometry; chapter 9 - UNITARY SPACES; 9.1. Hermitian Forms; 9.2. The Scalar Product in a Complex Space; 9.3. Normal Operators 327 $a9.4. Applications to Operator Theory in Euclidean Space 330 $a
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
410 0$aDover Books on Mathematics 606 $aAlgebras, Linear 606 $aMathematics$2HILCC 606 $aPhysical Sciences & Mathematics$2HILCC 606 $aAlgebra$2HILCC 615 0$aAlgebras, Linear. 615 7$aMathematics 615 7$aPhysical Sciences & Mathematics 615 7$aAlgebra 676 $a512/.5 700 $aShilov$b Georgi E$0349442 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911006800003321 996 $aLinear Algebra$94390570 997 $aUNINA