LU decomposition

LU decomposition is a mathematical process that breaks down a complex matrix into two simpler matrices: one (L) is lower triangular with zeros above the diagonal, and the other (U) is upper triangular with zeros below the diagonal. This technique makes solving systems of equations more efficient because it allows you to first solve for variables step-by-step using forward and backward substitution. Essentially, LU decomposition transforms a challenging problem into easier parts, simplifying calculations in linear algebra, data analysis, and engineering tasks.