Linear Algebra Crossword Puzzle

123456789101112131415161718192021222324252627
Across
  1. 1. The form associated to symmetric bilinear form B by Q(v) = B(v,v).
  2. 3. A linear operator N where N^r = 0 for some integer r.
  3. 6. The positive minus negative entries in a diagonalized matrix.
  4. 8. Subspace of linear functionals that evaluate to zero on a subset S.
  5. 9. The monic polynomial of smallest degree annihilating a matrix.
  6. 11. The polynomial defined by det(A - xI).
  7. 14. The subgroup of elements that a homomorphism maps to the identity.
  8. 15. A bijective linear function mapping one space to another.
  9. 18. A linear map f where the kernel consists only of the zero vector.
  10. 19. Group operation combining G1 and G2 into a set of pairs.
  11. 21. The space V/U consisting of all U-affine subsets.
  12. 23. A root of the characteristic polynomial.
  13. 26. A translated subspace subset, written as v + U.
  14. 27. An algebraic structure similar to a vector space, but over a ring.
Down
  1. 2. A group G where ab = ba for all elements.
  2. 4. A bilinear form with a non-trivial kernel.
  3. 5. Normal form for integer matrices where a diagonal entry divides the next.
  4. 7. The vector space V* consisting of all linear functionals.
  5. 10. A form on V that is linear in both of its variables.
  6. 11. Hamilton's partner in the theorem stating p_f(f) = 0.
  7. 12. The mathematician famous for the law of inertia.
  8. 13. Subgroup of elements x in an abelian group where cx = 0 for some c > 0.
  9. 16. Vectors u and v where B(u,v) = 0.
  10. 17. A complex bilinear form that is conjugate symmetric.
  11. 20. Bilinear form where B(u,v) = B(v,u).
  12. 22. An integer matrix with a determinant of exactly 1 or -1.
  13. 24. A finitely generated abelian group that has a basis.
  14. 25. A generalized eigenvector is formally known as this kind of vector.