ISBN13: | 9781032109381 |
ISBN10: | 1032109386 |
Kötéstípus: | Puhakötés |
Terjedelem: | 434 oldal |
Méret: | 254x178 mm |
Nyelv: | angol |
Illusztrációk: | 66 Illustrations, black & white; 1 Halftones, black & white; 65 Line drawings, black & white |
700 |
A matematika általános kérdései
Algebra
Optimalizáció, lineáris programozás, játékelmélet
Alkalmazott matematika
A számítástudomány elmélete, a számítástechnika általában
A matematika általános kérdései (karitatív célú kampány)
Algebra (karitatív célú kampány)
Optimalizáció, lineáris programozás, játékelmélet (karitatív célú kampány)
Alkalmazott matematika (karitatív célú kampány)
A számítástudomány elmélete, a számítástechnika általában (karitatív célú kampány)
Introduction To Linear Algebra
GBP 45.99
Kattintson ide a feliratkozáshoz
This book is designed for students who have never been exposed to the topics in a linear algebra course. The text is ?lled with interesting and diverse application sections but is also a theoretical text which aims to train students to do succinct computation in a knowledgeable way.
Introduction to Linear Algebra: Computation, Application, and Theory is designed for students who have never been exposed to the topics in a linear algebra course. The text is ?lled with interesting and diverse application sections but is also a theoretical text which aims to train students to do succinct computation in a knowledgeable way. After completing the course with this text, the student will not only know the best and shortest way to do linear algebraic computations but will also know why such computations are both e?ective and successful.
Features:
- Includes cutting edge applications in machine learning and data analytics
- Suitable as a primary text for undergraduates studying linear algebra
- Requires very little in the way of pre-requisites
"Exceptionally well organized and thoroughly 'student friendly' in presentation, Introduction To Linear Algebra: Computation, Application, and Theory is an ideal textbook for highschool, college, and university curriculums"
- Midwest Books Review
1. Examples of Vector Spaces. 1.1. First Vector Space: Tuples. 1.2. Dot Product. 1.3. Application: Geometry. 1.4. Second Vector Space: Matrices. 1.5. Matrix Multiplication. 2. Matrices and Linear Systems. 2.1. Systems of Linear Equations. 2.2. Gaussian Elimination. 2.3. Application: Markov Chains. 2.4. Application: The Simplex Method. 2.5. Elementary Matrices and Matrix Equivalence. 2.6. Inverse of a Matrix. 2.7. Application: The Simplex Method Revisited. 2.8. Homogeneous/Nonhomogeneous Systems and Rank. 2.9. Determinant. 2.10. Applications of the Determinant. 2.11. Application: Lu Factorization. 3. Vector Spaces. 3.1. Definition and Examples. 3.2. Subspace. 3.3. Linear Independence. 3.4. Span. 3.5. Basis and Dimension. 3.6. Subspaces Associated with a Matrix. 3.7. Application: Dimension Theorems. 4. Linear Transformations. 4.1. Definition and Examples. 4.2. Kernel and Image. 4.3. Matrix Representation. 4.4. Inverse and Isomorphism. 4.5. Similarity of Matrices. 4.6. Eigenvalues and Diagonalization. 4.7. Axiomatic Determinant. 4.8. Quotient Vector Space. 4.9. Dual Vector Space. 5. Inner Product Spaces. 5.1. Definition, Examples and Properties. 5.2. Orthogonal and Orthonormal. 5.3. Orthogonal Matrices. 5.4. Application: QR Factorization. 5.5. Schur Triangularization Theorem. 5.6. Orthogonal Projections and Best Approximation. 5.7. Real Symmetric Matrices. 5.8. Singular Value Decomposition. 5.9. Application: Least Squares Optimization. 6. Applications in Data Analytics. 6.1. Introduction. 6.2. Direction of Maximal Spread. 6.3. Principal Component Analysis. 6.4. Dimensionality Reduction. 6.5. Mahalanobis Distance. 6.6. Data Sphering. 6.7. Fisher Linear Discriminant Function. 6.8. Linear Discriminant Functions in Feature Space. 6.9. Minimal Square Error Linear Discriminant Function. 7. Quadratic Forms. 7.1. Introduction to Quadratic Forms. 7.2. Principal Minor Criterion. 7.3. Eigenvalue Criterion. 7.4. Application: Unconstrained Nonlinear Optimization. 7.5. General Quadratic Forms. Appendix A. Regular Matrices. Appendix B. Rotations and Reflections in Two Dimensions. Appendix C. Answers to Selected Exercises.