Linear Algebra Terms

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Across
  1. 4. the set <v1,...,vm> = {c1v1+...+cmvm | c1,...,cm ∈ R}
  2. 7. a bijective linear map T:V->W between vector spaces V and W
  3. 8. the subspace Eig_lm(T) sbs defined by Eiglmd(T) = {v ∈V | T(v) = lmbd v
  4. 9. summation (from i=1 ->n) aii
  5. 11. C[a,b] = {f:[a,b] -> R| f is a continuous function}
  6. 12. T(V) = {T(v) | v ∈V} is a subset of W
  7. 13. matrix A is ____ if there is an matrix A^-1 such that A A^-1 = A^-1 A = In
  8. 15. A ∈Mn(F) is similar to B ∈Mn(F) if there is an invertible S ∈Mn(F) for B = SAS^-1
  9. 16. needed to be true to have similar matrices: same rnak, null, list of eigenvalues, and trace
  10. 17. dimrangeT (maps), dimC(A) (matrices)
  11. 18. if a list of vectors is not linearly dependent
  12. 21. for any a1,a2∈A satisfying f(a) = f(a2), we have a1 = a2
  13. 23. T:V->W is a linear map and T is a ___ if it is additive and has homogeneity.
  14. 24. if a function is both injective and surjective
  15. 25. the span of the columns of A. If A = [a1 ... an], then C(A) = <a1,...,an>
  16. 27. dimkerT (maps), dimker(A) (matrices)
  17. 28. Pn(F) = {a0+a1x1+...+anxn | ai ∈ F}
Down
  1. 1. the set {v ∈V | T(v) = 0}
  2. 2. an nxm matrix if aij = 0 whenever i>j
  3. 3. the length of any basis of V
  4. 5. D[a,b] = {f:[a,b] -> R| f is a differentiable function}
  5. 6. a sum of vectors v1+...+vn with scalars c1,...,cn ∈ R such that c1v1+c2v2+...+cnvn ∈ R
  6. 10. if for any b ∈B, there exists a ∈A such that f(a) = b
  7. 14. if there exist scalars a1,...,an, not all 0, such that summation(j=1 -> n of ajvj = 0.
  8. 19. a list of vectors (v1, ..., vn) in V is a ___ if (v1, ..., vn) is linearly independent and spans V
  9. 20. if v!= (not equal) 0 and Tv = λv
  10. 22. if A is similar to a diagonal matrix, it is ___
  11. 26. a vector space is this if 0∈U, u1,u2∈U (then u1+u2∈U), and u ∈U (then cu ∈U)