"Hadamard's Maximum Determinant Problem" What is the maximum determinant value of 3x3 matrix whose entries consist of only 3 and 0.

Question

I'm currently studying linear algebra. I faced one question that bothers me so hard.

The question is about Hadamard's Maximum Determinant Problem.

Since I cannot understand the concept of this, I need understandable explanation with

following question.

• What is the maximum determinant value of 3x3 matrix whose entries consist of only 3 and 0.

I will keep watching on this post, so I wanna communicate with you about this question.

Thanks !

Answer 1

I used

$$\begin{pmatrix} 3&0&3\\ 3&3&0\\ 0&3&3\\ \end{pmatrix}$$

for a determinant of $3(9) + 0 + 3(9) = 54$. I wanted to maximize the determinants of minors with a positive sign, and for the negative one I chose to make the determinant 0.