Linear Algebra Problem BookAmerican Mathematical Soc., 1995/12/31 - 333 ページ Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer. |
目次
| 1 | |
2 VECTORS | 17 |
3 BASES | 39 |
4 TRANSFORMATIONS | 51 |
5 DUALITY | 85 |
6 SIMILARITY | 97 |
7 CANONICAL FORMS | 107 |
8 INNER PRODUCT SPACES | 129 |
Chapter 2 Vectors | 204 |
Chapter 3 Bases | 215 |
Chapter 4 Transformations | 227 |
Chapter 5 Duality | 250 |
Chapter 6 Similarity | 257 |
Chapter 7 Canonical Forms | 275 |
Chapter 8 Inner Product Spaces | 294 |
Chapter 9 Normality | 308 |
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多く使われている語句
addition adjoint affine transformation algebra answer apply arbitrary associative assumed bases basis belongs called coefficients commutative complement complex Conclusion Consequence consider consisting contains corresponding course defined definition dependent determinant diagonal dimension easy eigenvalue elements entries equal equation equivalent example exist fact field finite finite-dimensional follows given happens Hermitian Hint identity implies important independent inner product space instance integers invariant invertible less linear combination linear functional linear transformation look Mathematical matrix means modulo multiplication namely natural nilpotent normal notation Note obvious operation ordered pairs particular polynomial positive possible Problem projection proof prove question range real numbers reason relation replaced respect result scalar scalar multiple sense similar Solution span square statement subset subspace that‘s thing trivial true unitary vector space write yields zero