LU Decomposition is a mathematical technique used to factor a matrix into two simpler matrices: L and U. Here, L is a lower triangular matrix, meaning all the entries above the diagonal are zero, while U is an upper triangular matrix, where all the entries below the diagonal are zero. This decomposition simplifies solving systems of linear equations, as it allows for easier calculations. The primary advantage of LU Decomposition is that it can reduce the computational complexity when solving multiple systems of equations with the same coefficient matrix. Once the matrices L and U are computed, they can be reused, making the process more efficient in various applications, including numerical analysis and computer graphics.