Linear Algebra with Applications
by Jeffrey Holt
2nd Edition
Publisher: W.H. Freeman & Company
Book Details
| Print ISBN | 9781464193347 |
| eText ISBN | 9781319057695 |
| Publisher | W.H. Freeman & Company |
| Publishing Year | 2017 |
| Edition | 2nd Edition |
| Language | English |
| Pages | 576 |
Linear Algebra with Applications, 2nd Edition, written by Jeffrey Holt, is a mathematics textbook that provides systematic coverage of core linear algebra principles and computational matrix methods. The text establishes basic algebraic frameworks through theoretical structures and computational exercises.
Chapter 1 focuses on systems of linear equations, examining lines, linear systems, and matrices alongside numerical solutions and direct applications. The material extends into Euclidean space and matrix operations, building toward formal treatments of subspaces and determinants.
Subsequent chapters investigate eigenvalues, eigenvectors, and general vector spaces. Published by W.H. Freeman & Company in 2017, this 576-page volume organizes its foundational content across eleven structured chapters.
Table of Contents
Chapter 1: Systems of Linear Equations
- • 1.1 Lines and Linear Equations
- • 1.2 Linear Systems and Matrices
- • 1.3 Applications of Linear Systems
- • 1.4 Numerical Solutions
Chapter 2: Euclidean Space
- • 2.1 Vectors
- • 2.2 Span
- • 2.3 Linear Independence
Chapter 3: Matrices
- • 3.1 Linear Transformations
- • 3.2 Matrix Algebra
- • 3.3 Inverses
- • 3.4 LU Factorization
- • 3.5 Markov Chains
Chapter 4: Subspaces
- • 4.1 Introduction to Subspaces
- • 4.2 Basis and Dimension
- • 4.3 Row and Column Spaces
- • 4.4 Change of Basis
Chapter 5: Determinants
- • 5.1 The Determinant Function
- • 5.2 Properties of the Determinant
- • 5.3 Applications of the Determinant
Chapter 6: Eigenvalues and Eigenvectors
- • 6.1 Eigenvalues and Eigenvectors
- • 6.2 Diagonalization
- • 6.3 Complex Eigenvalues and Eigenvectors
- • 6.4 Systems of Differential Equations
- • 6.5 Approximation Methods
Chapter 7: Vector Spaces
- • 7.1 Vector Spaces and Subspaces
- • 7.2 Span and Linear Independence
- • 7.3 Basis and Dimension
Chapter 8: Orthogonality
- • 8.1 Dot Products and Orthogonal Sets
- • 8.2 Projection and the Gram-Schmidt Process
- • 8.3 Diagonalizing Symmetric Matrices and QR Factorization
- • 8.4 The Singular Value Decomposition
- • 8.5 Least Squares Regression
Chapter 9: Linear Transformations
- • 9.1 Definition and Properties
- • 9.2 Isomorphisms
- • 9.3 The Matrix of a Linear Transformation
- • 9.4 Similarity
Chapter 10: Inner Product Spaces
- • 10.1 Inner Products
- • 10.2 The Gram-Schmidt Process Revisited
- • 10.3 Applications of Inner Products
Chapter 11: Additional Topics and Applications
- • 11.1 Quadratic Forms
- • 11.2 Positive Definite Matrices
- • 11.3 Constrained Optimization
- • 11.4 Complex Vector Spaces
- • 11.5 Hermitian Matrices
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▶Research Sources (14)
- Linear Algebra with Applications
- EBOOK - (Loose Leaf) Linear Algebra with Applications (2E 17)
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- Koha online catalog › Details for: Linear algebra with applications /
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- Linear Algebra with Applications - Exercise 37, Ch 3, Pg 166
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- Linear Algebra with Applications - 2nd Edition - Solutions and Answers
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- Linear Algebra with Applications, 2nd Edition - Answer key
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