For solving a linear system,
$Ax = b$.
If $A$ is a dense but symmetric $n \times n$ matrix, how much memory is required?
$A$ is symmetric, which means only the upper (or lower) triangular part of $n \times (n+1)/2$ entries would be necessary. Does $A$'s memory requirement have to be 8 bytes $\times n \times n$ or can it be lowered toward 8 bytes $\times n \times (n+1)/2$?