
Rattle space equations
female robotic voice, mutation funk, bounce drop, power
May 6th, 2024suno
Lyrics
Axiom Statement
Associativity of vector addition u + (v + w) = (u + v) + w
Commutativity of vector addition u + v = v + u
Identity element of vector addition There exists an element 0 ∈ V, called the zero vector, such that v + 0 = v for all v ∈ V.
Inverse elements of vector addition For every v ∈ V, there exists an element −v ∈ V, called the additive inverse of v, such that v + (−v) = 0.
Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v [nb 3]
Identity element of scalar multiplication 1v = v, where 1 denotes the multiplicative identity in F.
Distributivity of scalar multiplication with respect to vector addition a(u + v) = au + av
Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv
Linear independence
The elements of a subset G of a F-vector space V are said to be linearly independent if no element of G can be written as a linear combination of the other elements of G. Equivalently, they are linearly independent if two linear combinations of elements of G define the same element of V if and only if they have the same coefficients. Also equivalently, they are linearly independent if a linear combination results in the zero vector if and only if all its coefficients are zero.
Functions from any fixed set Ω to a field F also form vector spaces, by performing addition and scalar multiplication pointwise. That is, the sum of two functions f and g is the function
(𝑓+𝑔){\displaystyle (f+g)} given by
[drop]
[outro]
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