Matrix A = LU Decompose
LU decompose - a square matrix A that can be expressed as product of L and U matrix, is called LU decomposition. A = LU Matrix L - It is called Lower triangular Matrix , whose elements above the main diagonal is zero valued elements. Matrix U - It is called Upper Triangular Matrix , whose elements below the main diagonal is zero valued elements. How to LU decompose - a square matrix A is decomposed or factorized into L and U matrix by elementary row operation , such as swapping two rows and adding or subtracting row by a scalar value. Application of LU decompose It is useful to find solution of system of linear equation and matrix inverse. Algorithm steps for A= LU decompose Read matrix A U = copy (A) L = Identity-matrix() i,j - position of a element in the matrix For i=1 To N Eor j=i+1 To N lambda=U ji /U ii R j <- R j - lambda