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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 !

uwu
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1 Answers1

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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.

pjs36
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  • Thanks for your comment. However, I want to solve this question by using Hadamard's method. (I tried to find the maximum value by using the same method that you used, and it works.) Can you tell me how to solve this question by using Hadamard's method? Thanks again :) – uwu Feb 22 '15 at 00:34
  • @JasonYu Ah, I didn't realize there was a such a method. – pjs36 Feb 22 '15 at 00:39