CotsSense

Matrices are fundamental objects in modern mathematics and invariably appear in all branches of science. An introductory use case for matrices is in solving linear systems like Ax = b . While this system is introductory and may feel toy'ish, such linear systems are at the center of most engineering problems.  Formulating a system into a linear matrix expression ( Ax = b ) is beyond the scope of this blog (may be covered in future). In this post, we will talk about a matrix factorization technique called $LU$ decomposition and its special case the Cholesky decomposition . These decomposition techniques help in transforming the original matrix expression into a simpler expression that gives solution x of the linear system Ax = b in an easy way. Consider the following two options for matrix $A$ In the case of $A_2$, owing to the upper triangular structure of the matrix solving for x is straightforward via substitution. The LU decomposition provides us with such an upper triangular...