Linear algebra /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Shilov, G. E. (Georgiĭ Evgenʹevich)
Formato: Electrónico eBook
Idioma:Inglés
Ruso
Publicado: New York : Dover Publications, 1977.
Edición:Rev. English ed. /
Colección:Dover books on mathematics.
Temas:
Algebras, Linear.
Algèbre linéaire.
Algebras, Linear
Álgebra linear.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine derived contents note: chapter 1
  • Determinants
  • 1.1. Number Fields
  • 1.2. Problems of the Theory of Systems of Linear Equations
  • 1.3. 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
  • Problems
  • 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 Spaces
  • Problems
  • chapter 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 Compatability 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
  • Problems
  • chapter 4
  • Linear Functions Of A Vector Argument
  • 4.1. Linear Forms
  • 4.2. Linear Operators
  • 4.3. Sums and Products of Linear 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
  • 4.8. Invariant Subspaces
  • 4.9. Eigenvectors and Eigenvalues
  • Problems
  • 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
  • Problems
  • 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
  • Problems
  • 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
  • Problems
  • 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
  • Problems
  • chapter 9
  • Unitary Spaces
  • 9.1. Hermitian Forms
  • 9.2. The Scalar Product in a Complex Space
  • 9.3. Normal Operators
  • 9.4. Applications to Operator Theory in Euclidean Space
  • Problems
  • chapter 10
  • Quadratic Forms In Euclidean And Unitary Spaces
  • 10.1. Basic Theorem on Quadratic Forms in a Euclidean Space
  • 10.2. Extremal Properties of a Quadratic Form
  • 10.3 Simultaneous Reduction of Two Quadratic Forms
  • 10.4. Reduction of the General Equation of a Quadratic Surface
  • 10.5. Geometric Properties.

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