A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, 2006 To book contents

5. Algebra

• 5.1. Polynomials and Algebraic Equations
  • 5.1.1. Polynomials and Their Properties
  • 5.1.2. Linear and Quadratic Equations
  • 5.1.3. Cubic Equations
  • 5.1.4. Fourth-Degree Equation
  • 5.1.5. Algebraic Equations of Arbitrary Degree and Their Properties
• 5.2. Matrices and Determinants
  • 5.2.1. Matrices
  • 5.2.2. Determinants
  • 5.2.3. Equivalent Matrices. Eigenvalues
• 5.3. Linear Spaces
  • 5.3.1. Concept of a Linear Space. Its Basis and Dimension
  • 5.3.2. Subspaces of Linear Spaces
  • 5.3.3. Coordinate Transformations Corresponding to Basis Transformations in a Linear Space
• 5.4. Euclidean Spaces
  • 5.4.1. Real Euclidean Space
  • 5.4.2. Complex Euclidean Space (Unitary Space)
  • 5.4.3. Banach Spaces and Hilbert Spaces
• 5.5. Systems of Linear Algebraic Equations
  • 5.5.1. Consistency Condition for a Linear System
  • 5.5.2. Finding Solutions of a System of Linear Equations
• 5.6. Linear Operators
  • 5.6.1. Notion of a Linear Operator. Its Properties
  • 5.6.2. Linear Operators in Matrix Form
  • 5.6.3. Eigenvectors and Eigenvalues of Linear Operators
• 5.7. Bilinear and Quadratic Forms
  • 5.7.1. Linear and Sesquilinear Forms
  • 5.7.2. Bilinear Forms
  • 5.7.3. Quadratic Forms
  • 5.7.4. Bilinear and Quadratic Forms in Euclidean Space
  • 5.7.5. Second-Order Hypersurfaces
• 5.8. Some Facts from Group Theory
  • 5.8.1. Groups and Their Basic Properties
  • 5.8.2. Transformation Groups
  • 5.8.3. Group Representations
• References for Chapter 5

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