MAT-2320: The 10 Vector Axioms

Card Set Information

Author:
UndependableAids
ID:
304749
Filename:
MAT-2320: The 10 Vector Axioms
Updated:
2015-07-03 13:24:21
Tags:
Vector Linear Algebra scalar additive axioms
Folders:
MAT-2320
Description:
Used for studying the 10 vector axioms in order to identify if the vector is considered a vector space.
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  1. closure under addition
    u + v ∈ R
  2. commutative property of addition
    u + v = v + u
  3. associative property of addition
    (u + v) + w = w + (v + w)
  4. additive identify property
    u + 0 = u
  5. additive inverse property
    u + (-u) = 0
  6. closure under scalar multiplication
    cu ∈ Rn
  7. associative property of multiplication
    c(du) = (cd)u
  8. distributive property of multiplication 1
    (c + d)u = cu + du
  9. distributive property of multiplication 2
    c(u + v) = cu + cv
  10. multiplicative identify property
    1*u = u

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