- #1
- 22,089
- 3,291
- Author: Howard Anton
- Title: Elementary Linear Algebra
- Amazon Link: https://www.amazon.com/dp/0470458216/?tag=pfamazon01-20&tag=pfamazon01-20
- Prerequisities: High-school mathematics
- Level: Undergrad
Table of Contents:
Code:
[LIST]
[*] Systems of Linear Equations and Matrices
[LIST]
[*] Introduction to systems of Linear Equations
[*] Gaussian Elimination
[*] Matrices and Matrix Operations
[*] Inverses; Algebraic Properties of Matrices
[*] Elementary Matrices and a Method for Finding [itex]A^{-1}[/itex]
[*] More on Linear Systems and Invertible Matrices
[*] Diagonal, Triangular, and Symmetric Matrices
[*] Application: Applications of Linear Systems
[*] Application: Leontief Input-Output Models
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[*] Determinants
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[*] Determinants by Cofactor Expansion
[*] Evaluating Determinants by Row Reduction
[*] Properties of Determinants; Cramer's Rule
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[*] Euclidean Vector Spaces
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[*] Vectors in 2-Space, 3-Space, and n-Space
[*] Norm, Dot Product, and Distance in R^n
[*] Orthogonality
[*] The Geometry of Linear Systems
[*] Cross Product
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[*] General Vector Spaces
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[*] Real Vector Spaces
[*] Subspaces
[*] Linear Independence
[*] Coordinates and Basis
[*] Dimension
[*] Change of Basis
[*] Row Space, Column Space, and Null Space
[*] Rank, Nullity, and the Fundamental Matrix Spaces
[*] Matrix Transformations from R^n to R^m
[*] Properties of Matrix Transformations
[*] Geometry of Matrix Operators in R^2
[*] Dynamical Systems and Markov Chains
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[*] Eigenvalues and Eigenvectors
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[*] Eigenvalues and Eigenvectors
[*] Diagonalization
[*] Complex Vector Spaces
[*] Application: Differential Equations
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[*] Inner Product Spaces
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[*] Inner Products
[*] Angle and Orthogonality in Inner Product Spaces
[*] Gram-Schmidt Process; QR-Decomposition
[*] Best Approximation; Least Squares
[*] Application: Least Squares Fitting to Data
[*] Application: Function Approximation; Fourier Series
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[*] Diagonalization and Quadratic Forms
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[*] Orthogonal Matrices
[*] Orthogonal Diagonalization
[*] Quadratic forms
[*] Optimization Using Quadratic Forms
[*] Hermitian, Unitary, and Normal Matrices
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[*] Linear Transformations
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[*] General Linear Transformations
[*] Isomorphism
[*] Compositions and Inverse Transformations
[*] Matrices for General Linear Transformations
[*] Similarity
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[*] Numerical Methods
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[*] LU-Decompositions
[*] The Power Method
[*] Application: Internet Search Engines
[*] Comparison of Procedures for Solving Linear Systems
[*] Singular Value DEcomposition
[*] Application: Data Compression Using Singular Value Decomposition
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[*] Appendix: How to Read Theorems
[*] Appendix: Complex Numbers
[*] Answers to Exercises
[*] Index
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