Vectors are in a lot of places and not just in maths, however I believe in maths the definition of a vector is the best, as it encompasses most other forms of vectors (in physics, a vector has a magnitude and a direction, but this is not the definition mathematicians use). The definition of a vector, is something that is “linear”, meaning that it can be added to and scaled up. With this more general definition. I can say that v : v = [people, fruit] is a vector, but does not have a direction. v_1 = [2(me+you),2(apples)] is a vector, and it has been scaled and added to.
For the most part, we will use vectors in Rn or Cn
- :journal: first entry for the previous year!Cauchy’s Theorem states |u · v| ≤ ||u||||v||
The Vector s ∈ ℝ3 = (x, y, z). x is a coordinate, entry or component
A linear span is the collection of all linear combinations of the vectors in question. for example the ,u, v ∈ ℝn, span(u, v) = {αu + βv} ∀α, β ∈ 𝔽
A linear combination is an element in the span
linear span := The span of v, u, ... ∈ 𝔽n
is the set A = {av + bu + ...}
where a, b, ... are
scalars in 𝔽 # examples $\begin{pmatrix} 1 & 2 & 3
\end{pmatrix}$ $\begin{pmatrix} 0 &
0 & 0 \end{pmatrix}$ see
https://www.youtube.com/watch?v=fNk_zzaMoSs as this gives a better
explaination of what is a vector. tags
:math:linear_algebra_1:linear_algebra_2: