Linear algebra with applications

Linear algebra with applications

For sophomore-level orjunior/senior-level first courses in linear algebra; assumes calculus as aprerequisite.   A thorough and accessibleintroduction to linear algebra. The new 10thEdition of Linear Algebra with Applications continuesto encourage a challenging and broad understanding of the subject....

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Detalles Bibliográficos
Otros Autores: Leon, Steven J. author (author), Pillis, Lisette G. de, author
Formato: Libro electrónico
Idioma:Inglés
Publicado: Harlow, England : Pearson Education, Limited [2021]
Edición:Tenth edition Global edition
Materias:
Algebra.
Àlgebra lineal
Libros electrónicos.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009667026806719
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright
  • Dedication
  • Contents
  • Preface
  • Chapter 1: Matrices and Systems of Equations
  • 1.1 Systems of Linear Equations
  • 1.2 Row Echelon Form
  • 1.3 Matrix Arithmetic
  • 1.4 Matrix Algebra
  • 1.5 Elementary Matrices
  • 1.6 Partitioned Matrices
  • Chapter 1 Exercises
  • MATLAB Exercises
  • Chapter Test A: True or False
  • Chapter Test B
  • Chapter 2: Determinants
  • 2.1 The Determinant of a Matrix
  • 2.2 Properties of Determinants
  • 2.3 Additional Topics and Applications
  • Chapter 2 Exercises
  • MATLAB Exercises
  • Chapter Test A True or False
  • Chapter Test B
  • Chapter 3: Vector Spaces
  • 3.1 Definition and Examples
  • 3.2 Subspaces
  • 3.3 Linear Independence
  • 3.4 Basis and Dimension
  • 3.5 Change of Basis
  • 3.6 Row Space and Column Space
  • Chapter 3 Exercises
  • MATLAB Exercises
  • Chapter Test A True or False
  • Chapter Test B
  • Chapter 4: Linear Transformations
  • 4.1 Definition and Examples
  • 4.2 Matrix Representations of Linear Transformations
  • 4.3 Similarity
  • Chapter 4 Exercises
  • MATLAB Exercises
  • Chapter Test A True or False
  • Chapter Test B
  • Chapter 5: Orthogonality
  • 5.1 The Scalar Product in Rn
  • 5.2 Orthogonal Subspaces
  • 5.3 Least Squares Problems
  • 5.4 Inner Product Spaces
  • 5.5 Orthonormal Sets
  • 5.6 The Gram-Schmidt Orthogonalization Process
  • 5.7 Orthogonal Polynomials
  • Chapter 5 Exercises
  • MATLAB Exercises
  • Chapter Test A True or False
  • Chapter Test B
  • Chapter 6: Eigenvalues
  • 6.1 Eigenvalues and Eigenvectors
  • 6.2 Systems of Linear Differential Equations
  • 6.3 Diagonalization
  • 6.4 Hermitian Matrices
  • 6.5 The Singular Value Decomposition
  • 6.6 Quadratic Forms
  • 6.7 Positive Definite Matrices
  • 6.8 Nonnegative Matrices
  • Chapter 6 Exercises
  • MATLAB Exercises
  • Chapter Test A True or False
  • Chapter Test B
  • Chapter 7: Numerical Linear Algebra.
  • 7.1 Floating-Point Numbers
  • 7.2 Gaussian Elimination
  • 7.3 Pivoting Strategies
  • 7.4 Matrix Norms and Condition Numbers
  • 7.5 Orthogonal Transformations
  • 7.6 The Eigenvalue Problem
  • 7.7 Least Squares Problems
  • 7.8 Iterative Methods
  • Chapter 7 Exercises
  • MATLAB Exercises
  • Chapter Test A True or False
  • Chapter Test B
  • Chapter 8: Canonical Forms
  • 8.1 Nilpotent Operators
  • 8.2 The Jordan Canonical Form
  • Appendix: MATLAB
  • Bibliography
  • Answers to Selected Exercises
  • Index.

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