Sorry, no online dictionaries contain the exact phrase category of vector spaces.
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Reverse dictionary results:
1. vector algebra
2. dual
3. basis
4. clas
5. position
6. dimension
7. dimensionality
8. dimensionally
9. dimensioning
10. ablation
11. acacia
12. crotchet
13. dickey
14. drive
15. entrance
16. jitney
17. magi
18. mandolin
19. mineralogist
20. piccolo
21. portal
22. positioning
23. stradivarius
24. surname
25. violin
26. waf
27. field
28. index
29. class
30. designate
31. occupation
32. order
33. shell
34. area
35. close
36. lattice
37. acne
38. baas
39. bagworm
40. baritone

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You can look up the words in the phrase individually using these links:   category ?   of ?   vector ?   spaces ?
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