2-1. 선형방정식과 선형시스템

본 글은 주재걸교수님의 인공지능을 위한 선형대수 강의를 듣고 정리한 내용입니다.

 

• Linear Equation

Other expression method

 

• Linear System : Set of Equations

• Identity Matrix(In)
  • A square matrix whose diagonal entries are all 1's, and the other entries are zeros.
• Inverse Matrix
  • For a square matrix A, its inverse matrix A^-1
  • A^-1A = AA^-1 = In

    

    Inverse Matrix

• Solving Linear System via Inverse Matrix

 

•  Non-Invertible Matrix A for 𝐴𝐱 = 𝐛
  • if A is invertible, the solution is x = A^-1b
  •  
  • ad - bc is called the determinant of A, detA
  • detA determines whether A is invertible
  • if 𝐴 is non-invertible, 𝐴𝐱 = 𝐛 will have either no solution or infinitely many solutions.

 

• Rectangular Matrix 𝐴 in 𝐴𝐱 = b
  • Recall 𝑚 = #equations and 𝑛 = #variables.
  • 𝑚 < 𝑛: more variables than equations
    • Usually infinitely many solutions exist (under-determined system).
  • 𝑚 > 𝑛: more equations than variables
    • Usually no solution exists (over-determined system).

 

 

 

출처: https://www.edwith.org/ai251 

인공지능을 위한 선형대수 강좌소개 : edwith

참고자료

https://www.cuemath.com/algebra/linear-equations/ 

https://blog.naver.com/PostView.naver?blogId=gpark0303&logNo=221780548151&parentCategoryNo=&categoryNo=10&viewDate=&isShowPopularPosts=false&from=postView