# linear algebra bounds?

• Dec 8th 2011, 06:29 PM
alphabeta89
linear algebra bounds?
Assume A is a general ${n}\times{n}$ matrix with entries $\left | a_{ij} \right |\leq1$ for $1\leq i,j \leq n$. Prove that the matrix $U$ in the $PA=LU$ factoriation satisfies $\left | a_{ij} \right |\leq 2^{n-1}$ for all $1\leq i,j \leq n$.