Sorry, no online dictionaries contain the exact phrase finite dimensional vector space.

Reverse dictionary results:
1. polytope
2. dimension
3. area
4. flat
5. hyperplane
6. field
7. projection
8. volume
9. normed
10. functional
11. spherical coordinates
12. dimensionality
13. dimensioning
14. curve
15. hyperboloid
16. simplex
17. content
18. solid
19. bulk
20. torus
21. terminate
22. wedge
23. line
24. measure
25. narrow
26. point
27. reach
28. reaches
29. reaching
30. neck
31. spacing
32. blank
33. virtually
34. dual
35. basis
36. null-space
37. norm
38. subspace
39. vector field
40. dimensionally

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You can look up the words in the phrase individually using these links:   finite ?   dimensional ?   vector ?   space ?
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