5,849
edits
Line 567: | Line 567: | ||
| 11.16 || Exercises || 443 | | 11.16 || Exercises || 443 | ||
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! colspan="3" | | ! colspan="3" | 12. VECTOR ALGEBRA | ||
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| 1 || | | 12.1 || Historical introduction || 445 | ||
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| 2 || | | 12.2 || The vector space of n-tuples of real numbers || 446 | ||
|- | |- | ||
| 3 || | | 12.3 || Geometric interpretation for \(n \leq 3\) || 448 | ||
|- | |- | ||
| 12.4 || Exercises || 450 | |||
|- | |- | ||
| | | 12.5 || The dot product || 451 | ||
|- | |- | ||
| 2 || | | 12.6 || Length or norm of a vector|| 453 | ||
|- | |||
| 12.7 || Orthogonality of vectors || 455 | |||
|- | |||
| 12.8 || Exercises || 456 | |||
|- | |||
| 12.9 || Projections. Angle between vectors in n-space || 457 | |||
|- | |||
| 12.10 || The unit coordinate vectors || 458 | |||
|- | |||
| 12.11 || Exercises || 460 | |||
|- | |||
| 12.12 || The linear span of a finite set of vectors || 462 | |||
|- | |||
| 12.13 || Linear independence || 463 | |||
|- | |||
| 12.14 || Bases || 466 | |||
|- | |||
| 12.15 || Exercises || 467 | |||
|- | |||
| 12.16 || The vector space \(V_N(C)\) of n-tuples of complex numbers || 468 | |||
|- | |||
| 12.17 || Exercises || 470 | |||
|- | |||
! colspan="3" | 13. APPLICATIONS OF VECTOR ALGEBRA TO ANALYTIC GEOMETRY | |||
|- | |||
| 1 || Introduction || 471 | |||
|- | |||
| 2 || Lines in n-space || 472 | |||
|- | |- | ||
! colspan="3" | Chapter 16: Induction and Summations | ! colspan="3" | Chapter 16: Induction and Summations |