Linear algebra - Lax, Peter D. (New York : John Wiley, 1997)
This introduction to linear algebra by world renowned mathematician Peter Lax is unique in its emphasis on the analytical aspects of the subject as well as its numerous applications. The book grew out of Dr. Lax's course notes for the linear algebra classes he teaches at New York University. Geared to graduate students as well as advanced undergraduates, it assumes only limited knowledge of linear algebra and avoids subjects already heavily treated in other textbooks.
And while it discusses linear equations, matrices, determinants, and vector spaces, it also includes a number of exciting topics that are not covered elsewhere, such as eigenvalues, the Hahn-Banach theorem, geometry, game theory, and numerical analysis. Clear, concise, and superbly organized. Linear Algebra is an excellent text for advanced undergraduate and graduate courses and also serves as a handy professional reference.
1. Fundamentals -- 2. Duality -- 3. Linear Mappings -- 4. Matrices -- 5. Determinant and Trace -- 6. Spectral Theory -- 7. Euclidean Structure -- 8. Spectral Theory of Selfadjoint Mappings -- 9. Calculus of Vector and Matrix Valued Functions -- 10. Matrix Inequalities -- 11. Kinematics and Dynamics -- 12. Convexity -- 13. The Duality Theorem -- 14. Normed Linear Spaces -- 15. Linear Mappings between Normed Spaces -- 16. Positive Matrices -- 17. How to Solve Systems of Linear Equations -- App. 1. Special Determinants -- App. 2. Pfaff's Theorem -- App. 3. Symplectic Matrices -- App. 4. Tensor Product -- App. 5. Lattices -- App. 6. Fast Matrix Multiplication -- App. 7. Gershgorin's Theorem -- App. 8. The Multiplicity of Eigenvalues.
"A Wiley-Interscience publication."
Includes bibliographical references (p. 245) and index.
Keywords: Algebras, Linear