Linear algebra
Author(s)
Bibliographic Information
Linear algebra
(Always learning)
Pearson Education, c2014
4th ed., New International ed.
- : pbk
- Other Title
-
Pearson new international edition
Available at 1 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
"Pearson custom library"--Table of contents
Includes indexes
Description and Table of Contents
Description
For courses in Advanced Linear Algebra. This top-selling, theorem-proof text presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.
Table of Contents
1. Vector Spaces.
Introduction. Vector Spaces. Subspaces. Linear Combinations and Systems of Linear Equations. Linear Dependence and Linear Independence. Bases and Dimension. Maximal Linearly Independent Subsets.
2. Linear Transformations and Matrices.
Linear Transformations, Null Spaces, and Ranges. The Matrix Representation of a Linear Transformation. Composition of Linear Transformations and Matrix Multiplication. Invertibility and Isomorphisms. The Change of Coordinate Matrix. Dual Spaces. Homogeneous Linear Differential Equations with Constant Coefficients.
3. Elementary Matrix Operations and Systems of Linear Equations.
Elementary Matrix Operations and Elementary Matrices. The Rank of a Matrix and Matrix Inverses. Systems of Linear Equations-Theoretical Aspects. Systems of Linear Equations-Computational Aspects.
4. Determinants.
Determinants of Order 2. Determinants of Order n. Properties of Determinants. Summary-Important Facts about Determinants. A Characterization of the Determinant.
5. Diagonalization.
Eigenvalues and Eigenvectors. Diagonalizability. Matrix Limits and Markov Chains. Invariant Subspaces and the Cayley-Hamilton Theorem.
6. Inner Product Spaces.
Inner Products and Norms. The Gram-Schmidt Orthogonalization Process and Orthogonal Complements. The Adjoint of a Linear Operator. Normal and Self-Adjoint Operators. Unitary and Orthogonal Operators and Their Matrices. Orthogonal Projections and the Spectral Theorem. The Singular Value Decomposition and the Pseudoinverse. Bilinear and Quadratic Forms. Einstein's Special Theory of Relativity. Conditioning and the Rayleigh Quotient. The Geometry of Orthogonal Operators.
Appendices.
Sets. Functions. Fields. Complex Numbers. Polynomials.
Answers to Selected Exercises.
Index.
by "Nielsen BookData"