Notation:
Computational cost: .
Two vectors and are orthogonal if .
For a subspace , we can define the orthogonal complement as the subspace of vectors such that:
We have: .
Nov 19, 20241 min read
Notation:
xTy=x1y1+⋯+xnynComputational cost: O(n).
Two vectors x and y are orthogonal if xTy=0.
For a subspace S, we can define the orthogonal complement S⊥ as the subspace of vectors y such that:
S⊥={y∣∀x∈S,xTy=0}We have: dim(S)+dim(S⊥)=n.