Question

what is a vector space and subspace what is a vector space and subspace @Mathematics

Answer 1

wikipedia is very helpful. http://en.wikipedia.org/wiki/Vector_space

Answer 2

Axiom Signification
Associativity of addition v1 + (v2 + v3) = (v1 + v2) + v3.
Commutativity of addition v1 + v2 = v2 + v1.
Identity element of addition There exists an element 0 ∈ V, called the zero vector, such that v + 0 = v for all v ∈ V.
Inverse elements of addition For all v ∈ V, there exists an element -v ∈ V, called the additive inverse of v, such that v + (-v) = 0.
Distributivity of scalar multiplication with respect to vector addition   s(v1 + v2) = sv1 + sv2.
Distributivity of scalar multiplication with respect to field addition (n1 + n2)v = n1v + n2v.
Respect of scalar multiplication over field's multiplication n1 (n2 s) = (n1 n2)s [nb 2]
Identity element of scalar multiplication 1s = s, where 1 denotes the multiplicative identity in F.

Answer 3

this space is vector space

Answer 4

any subset of this vector space satifsying same axioms over the same feild is subspace

Answer 5

Subspaces are vector spaces in their own right contained within the vector space. Just as "indeed" is a word, and the letters "deed" within indeed is also a word, so we call it a subword, but saying "sub-vector space" is too long-winded, so it's shortened to just subspace.

Answer 6

thnx 2 u oll....

Answer 7

a place where algebra of vectors makes sense