Introduction to linear algebra for science and engineering

Cover
Title Page
Copyright Page
Table of Contents
A Note to Students
A Note to Instructors
A Personal Note
Acknowledgments
Chapter 1: Euclidean Vector Spaces
	1.1. Vectors in R2 and R3
	1.2. Spanning and Linear Independence in R2 and R3
	1.3. Length and Angles in R2 and R3
	1.4. Vectors in Rn
	1.5. Dot Products and Projections in Rn
	Chapter Review
Chapter 2: Systems of Linear Equations
	2.1. Systems of Linear Equations and Elimination
	2.2. Reduced Row Echelon Form, Rank, and Homogeneous Systems
	2.3. Application to Spanning and Linear Independence
	2.4. Applications of Systems of Linear Equations
	Chapter Review
Chapter 3: Matrices, LinearMappings, and Inverses
	3.1. Operations onMatrices
	3.2. MatrixMappings and LinearMappings
	3.3. Geometrical Transformations
	3.4. Special Subspaces
	3.5. InverseMatrices and InverseMappings
	3.6. ElementaryMatrices
	3.7. LU-Decomposition
	Chapter Review
Chapter 4: Vector Spaces
	4.1. Spaces of Polynomials
	4.2. Vector Spaces
	4.3. Bases and Dimensions
	4.4. Coordinates
	4.5. General LinearMappings
	4.6. Matrix of a LinearMapping
	4.7. Isomorphisms of Vector Spaces
	Chapter Review
Chapter 5: Determinants
	5.1. Determinants in Terms of Cofactors
	5.2. Properties of the Determinant
	5.3. Inverse by Cofactors, Cramer’s Rule
	5.4. Area, Volume, and the Determinant
	Chapter Review
Chapter 6: Eigenvectors and Diagonalization
	6.1. Eigenvalues and Eigenvectors
	6.2. Diagonalization
	6.3. Applications of Diagonalization
	Chapter Review
Chapter 7: Inner Products and Projections
	7.1. Orthogonal Bases in Rn
	7.2. Projections and the Gram-Schmidt Procedure
	7.3. Method of Least Squares
	7.4. Inner Product Spaces
	7.5. Fourier Series
	Chapter Review
Chapter 8: SymmetricMatrices and Quadratic Forms
	8.1. Diagonalization of SymmetricMatrices
	8.2. Quadratic Forms
	8.3. Graphs of Quadratic Forms
	8.4. Applications of Quadratic Forms
	8.5. Singular Value Decomposition
	Chapter Review
Chapter 9: Complex Vector Spaces
	9.1. Complex Numbers
	9.2. Systems with Complex Numbers
	9.3. Complex Vector Spaces
	9.4. Complex Diagonalization
	9.5. Unitary Diagonalization
	Chapter Review
Appendix A: Answers toMid-Section Exercises
Appendix B: Answers to Practice Problems and Chapter Quizzes
Index
Index of Notations
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