Questions tagged [lu-decomposition]

To prove that if matrix $U$ is obtained from $A$ by the row operation $R_i = R_i + kR_j$, then $L$ is obtained from the identity matrix $I_n$ by the reverse row operation $R_i = R_i - kR_j$, such that $A = LU$, we can express $A$ as the product of…

Almost all square matrices have an (unpivoted) LU decomposition, but some don't. The question I have is whether - assuming $M$ is a square matrix over $\mathbb R$ or $\mathbb C$ which does not admit an LU decomposition - there is some scalar…

It's well known that matrices of the form $M^T M$ have an (unpivoted, of course) LU decomposition. In fact, because they are positive semidefinite, they have a Cholesky decomposition. The field here is the real numbers. My question is: Do matrices…

I have this question: what is the cost of computing LU decomposition for a symmetric matrix. I tried to compute it, however, I calculated it as $2n^2$ as follows: I considered the LDL decomposition, and I concluded for the $i$-th row, I need…