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LAFF. week 1 (3)basis (i, j ,k (e0,e1,e2), image, all elements except 1…

- - - - parallelogram
        
        x+y = y+x
      - ζ0 = χ0 + ψ0
        ...
        ζn = χn + ψn
  - - - axpy
        y = ax + y
      - αu + βv
        u, v ∈ R^n
        α, β ∈ R
      - s0Vo + s1V1 + ... + sn-1Vn-1
        
        vectors
        
        coefficients
        scalars
        
        χ0, χ1 ... χn-1
        
        V0, V1 ... Vn-1
        
        LC of m n-dim vectors
      - any vector X
        
        can be written
        
        as a LC
        
        of unit basis vectors!
      - result is a vector
    - - dot(x,y) = x'*y
        
        ζ0 = χ0 ψ0 +χ1 ψ1 +... +ζn = χnψn
      - projection
        
        v ⊥ w ⇐⇒ dot(v · w) = 0
        
        dot(b,a) = |b|*cos(T)*|a| = proj*|a|
        dot не длина самой проекции, а произведение проекции на длину вектора на который проецируем
      - result is a scalar
    - - ζ0 = sqrt( χ0χ0)
        ...
        ζn = sqrt(χnχ0n)
      - norm
      - i.e.
        
        seems like dot product, right?
        
        so length is a sqrt(dot(x,x))
- - - - ordered array