A CLASSIFICATION OF QUADRATIC VECTORS. 



By Frank Lauren Hitchcock. 



Received. May 8, 1916. 



CONTENTS. 



Page. 



Introduction 372 



Part One. 



Art. 



1. Addition of vectors 374 



2. Classification by means of axes 375 



3. Theorems on reducible vectors 376 



4. Transformations which leave axes unaltered 376 



5. Determination of the general vector by its axes 377 



6. Deductions from the model vector 384 



Part Two. Reducible Vectors. 



7. Subdivision of reducible vectors 386 



8. Theorems on vector forms 386 



9. Derivation of the three sub-t>T3es 388 



10. A negative theorem on reducible vectors 390 



Part Three. Vectors with Multiple Axes. 



11. First form of the condition for a double axis 392 



12. Second form of the condition for a double axis 396 



13. Method of limits applied to obtain a double axis 397 



14. Fourth method for obtaining a double axis 400 



15. Simultaneous double axes 400 



16. Summary of results on double axes 404 



17. First form of condition for a triple axis 404 



18. Working rule for a triple axis 405 



19. Third form of condition for a triple axis 408 



20. General rule for double and triple axes for vectors of any degree . 411 



21. Method of limits applied to obtain a triple axis 412 



22. Simultaneous triple and double axes 414 



23. Simultaneous triple axes 416 



24. Type-form related to point-transformations 420 



25. Summary of results on triple axes 420 



26-32. Quadruple axes 420 



Part Four. Factorization. 



33. Factoring the general quadratic vector 432 



34. Factoring vectors with double axes 435 



35. Factoring vectors with a triple axis 437 



36. Factoring vectors with two triple axes 439 



37. Factoring vectors with a quadruple axis 441 



38. Summary of results on factorization 454 



