Linear Algebra 119, Intersection of Subspaces, proof

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Linear Algebra 119, Intersection of Subspaces
  1. LadislauFernandes
  2. ideals Gröbner Bases for ideals extension fields vector spaces sylow theorems sylow theory
  3. automorphisms
  4. unique factorization domain
  5. homological algebra
  6. splitting fields
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Комментарии
Автор

👌👌👌👌 I came to know why element 0 belongs intersection of any family of subspace...
Tq u sir

saisameer
Автор

at 03:22 he needs to have also included "for all 'i' in 'I' ".
Without this inclusion, the conditional statement does not make sense, as there is no justification for why some linear combination of vectors in ONE subspace appears in 'W' as well.

(It is important to say that THAT linear combination of vectors appears in ALL subspaces, THEREFORE it of course must appear in 'W' as well.)

VishwaSharma
Автор

In 2), shouldn't it be:

"Since vector u and w are in the subspaces (w subscript i), vector u and w are also in the intersection (w)"?

What you proposed was "Since vector u and w are in the intersection (w), vector u and w are also in the subspaces (w subscript i)".

yan.weather