Linear Algebra: A First Course in Pure and Applied Math Edgar G. Goodaire
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Linear Algebra
Linear Algebra
Zusammenfassung
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 Zusammenfassung
Inhaltsverzeichnis
(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.
Zusätzliche Informationen
GOR013716600
9780130470171
0130470171
Linear Algebra: A First Course in Pure and Applied Math Edgar G. Goodaire
Gebraucht - Gut
Gebundene Ausgabe
Pearson Education (US)
2003-02-06
656
N/A
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