3-4. Orthogonal Projection

본 글은 주재걸교수님의 인공지능을 위한 선형대수 강의를 듣고 정리한 내용입니다.

 

 

the case of invertible 𝐶 = 𝐴^𝑇𝐴, consider the orthogonal projection of 𝐛 onto Col 𝐴 as

Orthogonal and Orthonormal Sets

orthogonal set if each pair of distinct vectors from the set is orthogonal That is, if 𝐮𝑖 ⋅ 𝐮𝑗 = 0 whenever 𝑖 ≠ 𝑗.

orthonormal set if it is an orthogonal set of unit vectors.

Orthogonal and Orthonormal Basis

subspace에 대한 basis 중 Orthogonal을 만족하는 Basis

Gram–Schmidt process

Orthogonal Projection 𝐲 ො of 𝐲 onto Line 

Orthogonal Projection 𝐲 ො of 𝐲 onto Plane

각 span에 대해 projection 한 후 더해주는 것과 같은 결과를 가진다.

Transformation: Orthogonal Projection

Consider a transformation of orthogonal projection 𝐛 መ of 𝐛, given orthonormal basis 𝐮1, 𝐮2 of a subspace W

 

 

 

출처: https://www.edwith.org/ai251