Linear Algebra: A First Course in Pure and Applied Math by Edgar G. Goodaire
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Linear Algebra
Summary
For freshman/sophomore-level courses in linear algebra.
This innovative new way of teaching a first linear algebra course stresses an Active Reading theme that teaches students to reach mathematics. A secondary theme of the text is much more applied: solving least square solutions to AX = b.
Linear Algebra Summary
Table of Contents
(NOTE: Each chapter concludes with Review Exercises.)
1. The Geometry of the Plane and 3 Space.
Vectors. Length and Direction. Lines, Planes, Cross Product. Projections. Euclidean n-space.
2. Matrices and Linear Equations.
The Algebra of Matrices. The Inverse and Transpose. Systems of Linear Equations. Homogeneous Systems and Linear Independence. The LU Factorization of a Matrix. LDU Factorizations. Finding the Inverse of a Matrix.
3. Determinants and Eigenvalues.
The Determinant of a Matrix. Properties of Determinants. The Eigenvalues and Eigenvectors of a Matrix. Similarity and Diagonalization.
4. Vector Spaces.
The Theory of Linear Equations. Basic Terminology and Concepts (Mostly Review). Basis and Dimensions; Rank and Nullity. One-sided Inverses.
5. Linear Transformations.
Fundamentals. Matrix Multiplication Revisited. The Matrices of a Linear Transformation. Changing Coordinates.
6. Orthogonality.
Projection Matrices and Least Square Approximation. The Gram-Schmidt Algorithm and QR Factorization. Orthogonal Subspaces and Complements. The Pseudoinverse of a Matrix.
7. The Spectral Theorem.
Complex Numbers and Vectors. Complex Matrices. Unitary Diagonalization. The Orthogonal Diagonalization of Real Symmetric Matrices. The Singular Value Decomposition.
8. Applications.
Data Fitting. Linear Recurrence Relations. Markov Processes. Quadratic Forms and Conic Sections. Graphs.
Show and Prove.
Things I Must Remember.
Solutions to Selected Exercises.
Solutions to True/False Questions.
Glossary.
Index.
1. The Geometry of the Plane and 3 Space.
Vectors. Length and Direction. Lines, Planes, Cross Product. Projections. Euclidean n-space.
2. Matrices and Linear Equations.
The Algebra of Matrices. The Inverse and Transpose. Systems of Linear Equations. Homogeneous Systems and Linear Independence. The LU Factorization of a Matrix. LDU Factorizations. Finding the Inverse of a Matrix.
3. Determinants and Eigenvalues.
The Determinant of a Matrix. Properties of Determinants. The Eigenvalues and Eigenvectors of a Matrix. Similarity and Diagonalization.
4. Vector Spaces.
The Theory of Linear Equations. Basic Terminology and Concepts (Mostly Review). Basis and Dimensions; Rank and Nullity. One-sided Inverses.
5. Linear Transformations.
Fundamentals. Matrix Multiplication Revisited. The Matrices of a Linear Transformation. Changing Coordinates.
6. Orthogonality.
Projection Matrices and Least Square Approximation. The Gram-Schmidt Algorithm and QR Factorization. Orthogonal Subspaces and Complements. The Pseudoinverse of a Matrix.
7. The Spectral Theorem.
Complex Numbers and Vectors. Complex Matrices. Unitary Diagonalization. The Orthogonal Diagonalization of Real Symmetric Matrices. The Singular Value Decomposition.
8. Applications.
Data Fitting. Linear Recurrence Relations. Markov Processes. Quadratic Forms and Conic Sections. Graphs.
Show and Prove.
Things I Must Remember.
Solutions to Selected Exercises.
Solutions to True/False Questions.
Glossary.
Index.
Additional information
GOR013716600
9780130470171
0130470171
Linear Algebra: A First Course in Pure and Applied Math by Edgar G. Goodaire
Used - Good
Hardback
Pearson Education (US)
2003-02-06
656
N/A
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This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us