Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
triangular matrix. What we get is: 𝐿𝑈𝑥=𝑏 Let 𝑦=𝑈𝑥 We can solve the equation 𝐿𝑦=𝑏 using forward substitution in 𝑂(𝑛^2) operations. And then we can solve 𝑈𝑥=𝑦 using back substitution in another 𝑂(𝑛^2) step. This reduces the time complexity to 𝑂(2*𝑛^2) steps. For large systems, this can reduce the