[Linear_Algebra] 3 types of Linear system equations

Today, we are going to discuss the three types of Linear System Equations (LSE). When the number of unknowns is equal to the number of equations, it is called a Square System. We can represent it as: A(n×n) X = b In this system, the solution is usually unique, but exceptions can exist. If the number of unknowns is greater than the number of equations, it is called an Under-constrained System.We..

[Linear_Algebra] Gauss Elimination & Gauss-Jordan Elimination

Today, we are going to talk about Gauss Elimination and Gauss–Jordan Elimination, which are crucial for solving linear equations. We discussed Gauss Elimination in the previous post. First of all, when GE is performed, the matrix is converted into Row Echelon Form. The next step is back substitution, which means going upward in the matrix to solve for the variables. On the other hand, when GJ is..

[Linear_Algebra] Gaussian elimination and LU factorization

Gaussian elimination(GE)를 이용해 linear equation의 해를 구할 수 있다.하지만, 이 과정을 컴퓨터 프로그래밍으로 계산하기 위해서는 행렬로 표현할 수 있어야 한다. 이때 사용하는 방법을 알아보자. 1. Elementary matrixLet A be the original matrix. 이런 조건에서 첫 번째 행을 상수배하여 두 번째 행에 더하거나 빼는 과정을 하게 된다. 이러한 연산 과정을 행렬로 나타낸 것을 E21이라고 한다. E21은 identity matrix에서 (2,1) 위치에 상수를 넣어 만든 행렬이다. 또 다른 예시로는 E32가 있다. 이 행렬은 identity matrix의 (3,2) 위치에 coefficient를 넣은 행렬이다.Elementary matri..

[Linear_algebra] Linearlity

What means linear? 1. f(x1 + x2) = f(x1) + f(x2) 2. f(cx1) = cf(x1) So, we are using this formula which equation meets linearlity f(ax1 + bx2) = af(x1) + bf(x2)