3-2 Least Squares와 그 기하학적 의미

본 글은 주재걸교수님의 인공지능을 위한 선형대수 강의를 듣고 정리한 내용입니다.

 

The most important aspect of the least-squares problem is that no matter what x we select, the vector 𝐴𝐱 will necessarily be in the column space Col 𝐴

 

Thus, we seek for x that makes 𝐴𝐱 as the closest point in Col 𝐴 to 𝐛.

𝐛 − 𝐴𝐱  ⊥ (𝑥1a1 + 𝑥2a2 ⋯ + 𝑥𝑝a𝑛) for any vector x

given a least squares problem, 𝐴𝐱 ≃ 𝐛, we obtain 

which is called a normal equation

 

 

 

출처: https://www.edwith.org/ai251