Vector Spaces: Definitions and Axioms

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Комментарии
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Explained Axioms extremely well without over-complicating. Highly recommend this video to others!

ayaanmunshi
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Was struggling to understand the axioms, highly appreciate the video!

visped
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Good video, and that trick to remember it, helped a lot.

sher.
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Very comprehensive video Quan! You may want to do a video explaining what a Field is, and what a Group is, as that would complement some of the abstract ideas that you touched on. Keep up the good work!

jamesmott
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Can you please upload the series of group theory!!

DargiShameer
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1.(V; F; +; •; "+"; *) = vector space V(F) over scalar field
(F; "+"; *)
2."Linear Transformations" left or right unary operators
• : V ---> V
3. Associative operations' interchange
(a*b)•v = a•(b•v)
; vector v and scalars a and b
4. Distributive operations' interchange
(a "+" b)•v =
a•v + b•v

mandlazulu
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1.
(V; F; 🇨🇭; 🇯🇵; +; *) = vector space V(F) over scalar field
(F; +; *)
2.Closure of Linear Transformation examples of left (or right) unary operator
🇯🇵 : V ---> V e.g. Left Constant Matrix multiplication of column vectors or Right Constant Matrix multiplication of row vectors.
3. Associative or communicable operators' interchange
(a*b)🇯🇵v =
a🇯🇵(b🇯🇵v)
; vector v and scalars a and b
4. Distributive operators' interchange
(a + b)🇯🇵v =
a🇯🇵v 🇨🇭 b🇯🇵v
5. Commutative or Abelian ("additive") groups (V; 🇨🇭) and (F; +)
6. Scientific Vector Space "Fields" e. g. Gravitational Force Vector Field, Electric and Magnetic Vector Space Fields.

mandlazulu
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Maaan been a while
I'm spamming like

bebarshossny