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Matrix For this particle Multiple Choice Question(more than one correct) Let B= $A^2$ The four 'B' matrix are represented in pics.'A' is the diagonal Matrix.

I am trying to undersrand this problem.

My issue is with Matrix D, even if used diagonal matrix and use entity [1,i,i] in the diagonal after squarring we get D matrix.

Is negative determinant or positive determinant a check for this type of problem as mentioned in the solution

Samar Imam Zaidi
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1 Answers1

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Have you tried calculating $$\begin{bmatrix}1&0&0\\0&0&1\\0&-1&0\end{bmatrix}^2$$and see what you get? Of course, if you want a diagonal matrix which squares to $D$, then it would have to have imaginary entries, but no one said the "square roots" would have to be diagonal matrices.

Arthur
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  • Put a11=1,a22=i,a33=i and then square it, what is the correct method of knowing wether the matrix is square of all real entities – Samar Imam Zaidi Aug 25 '17 at 09:03
  • @SamarImamZaidi Yes, that is one square root of $D$. But if you set $a_{22} = 0, a_{33} = 0, a_{23} = 1$ and $a_{32} = -1$ instead, you get another, with only real entries. – Arthur Aug 25 '17 at 09:05
  • I mean to say whether there is any check to prove that a particular matrix is a square of matrix with imaginary entries – Samar Imam Zaidi Aug 25 '17 at 09:09
  • @SamarImamZaidi If the matrix is either invertible or diagonalisable, it always has a complex square root. There are other matrices as well, but I don't think there's a simple classification of all of them. Possibly with Jordan normal form something could be done, but I have little experience with those personally. However, the original question wasn't "Is there a diagonal complex matrix which squares to this matrix", but rather "is there any real matrix which squares to this one". Since the matrix I've written above squares to the matrix $D$, there is a real matrix which squares to $D$. – Arthur Aug 25 '17 at 09:25
  • I have rephrased and redefined this question, is there any other example in this forum which solves my query – Samar Imam Zaidi Sep 06 '17 at 15:20