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Linear algebra / Georgi E. Shilov

By: Shilov, G. EMaterial type: Text

TextPublication details: New York : Dover Publications, 1977Description: xi, 387 p. 21 cmISBN: 9780486635187Subject(s): Algebras, LinearDDC classification: 512.5

Contents:

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. 2.7. 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. 4.6.The Range and Null Space of a Linear Operator 4.7. 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 . 6.2. Algebras. The Algebra of Polynomials 6.3. 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. 7.7. 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.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
General Books	Central Library, Sikkim University	512.5 SHI/L (Browse shelf(Opens below))	Available		47396

Total holds: 0

Original ed. published by Prentice-Hall, Englewood Cliffs, N.J.

Includes index.

Bibliography: p. 379.

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. 2.7. 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. 4.6.The Range and Null Space of a Linear Operator 4.7. 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 . 6.2. Algebras. The Algebra of Polynomials 6.3. 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. 7.7. 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.

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