2
$\begingroup$

Find the maximal determinant of a $4n \times 4n$ matrix with $2n$ entries equal to $1$ and $2n$ entries equal to $-1$.


My attempt:

For $n=1$, we take the following matrix:

\begin{pmatrix} 1 & 0 & -1 & -1 \\ 0 & 1 & 0 & 0\\ 0 & 0 & 2 & 0\\ 0 & 0 & 0 & 2 \end{pmatrix}

But, instead of $2$ I would put any other value, so does this determinant diverge?

$\endgroup$
3
  • 7
    $\begingroup$ Perhaps they meant "all the other entries must be zero". $\endgroup$
    – Trebor
    Commented May 8, 2023 at 13:31
  • $\begingroup$ Where does this problem come from? A book? Lecture notes? $\endgroup$ Commented May 8, 2023 at 15:06
  • $\begingroup$ What does the arrangement needs to satisfy in order for the determinant to be nonzero? $\endgroup$
    – AHusain
    Commented May 8, 2023 at 15:16

0

You must log in to answer this question.

Browse other questions tagged .