Introduction to Linear Algebra 2nd edition by Serge Lang ISBN ‎ 1461270022 978-1461270027

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Product details:

ISBN 10:‎ 1461270022
ISBN 13: 978-1461270027
Author: Serge Lang

This book is a short text in linear algebra, intended for a one-term course. Lang discusses the relation between the geometry and the algebra underlying the subject, and includes sections on linear equations, matrices and Gaussian elimination, and vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, and others are conceptual.

Introduction to Linear Algebra 2nd Table of contents:

• Introduction to Linear Algebra

  • Basic concepts and motivation for studying linear algebra
  • Vectors and their geometric interpretation
  • Linear systems and matrix representations

• Solving Linear Systems

  • Gaussian elimination
  • Row echelon form
  • Matrix inverses and their applications

• Vector Spaces

  • Definition and examples of vector spaces
  • Subspaces, bases, and dimensions
  • Linear independence and span

• Eigenvalues and Eigenvectors

  • The characteristic equation
  • Diagonalization of matrices
  • Applications of eigenvalues in various fields

• Orthogonality

  • Inner product spaces
  • Orthogonal projections and the Gram-Schmidt process
  • Least squares problems

• Determinants

  • Properties and computation of determinants
  • Cramer’s rule
  • The relationship between determinants and matrix invertibility

• Linear Transformations

  • Definition and properties of linear transformations
  • Matrix representations of linear transformations
  • Change of basis and coordinate systems

• Applications of Linear Algebra

  • Applications in computer graphics, data science, and machine learning
  • Linear algebra in engineering and physics

• Advanced Topics

  • Singular value decomposition (SVD)
  • Jordan form and its applications

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