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Aditi Agrawal posted an Question
June 02, 2020 • 22:48 pm 30 points
  • IIT JAM
  • Physics (PH)

Please explain this example.

3 Answer(s) Answer Now
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    Abhishek singh

    2) second method: it is the usual method of calculating Eigen value using characteristics equation.

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    Abhishek singh best-answer

    no other possible combinations existing such that all three properties can be satisfied simultaneously.

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    Abhishek singh Best Answer

    1)first method : as the given matrix is both symmetric as well as orthogonal. And we know that symmetric matrices have only real eigenvalues. hence eigenvalues must be real. Now, orthogonal matrices have eigenvalues whose modulus is one. it means you could have either 1 or -1 as the eigenvalues. now coming to the third property of matrix, trace of this matric is zero. and trace of matrix is equal to sum of all its eigenvalues. so the Eigen value must be such that their sum is zero. i.e. Eigen values are 1,1,-1,-1.

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    Abhishek singh best-answer

    this question is solved by two methods. first method is by using properties of symmetric and orthogonal matrices. and the second method is the usual method to find the eigenvalues.

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