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Aditi Agrawal posted an Question

June 03, 2020 • 13:47 pm

30 points

IIT JAM
Physics (PH)

Explain this example

3 Answer(s)

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Abhishek singh

now as you know the eigenvalues of matrix A of my solution. the eigenvalues of matrix B would be π/2 time the eigenvalues of matrix A. thats why I multiplied the eigenvalues of A by π/2 at the end, to get eigenvalues of B. which was asked to be calculated.
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Abhishek singh Best Answer

The given matrix is orthogonal, and skew symmetric. orthogonal matrices have Eigen values whose modulus is (1). and it is skew symmetric as well, which says it's eigenvalues must be either zero or purely imagination. considering both conditions, we can say, Eigen values could be iota or -iota only. then only both conditions will be satisfied simultaneously. now as the trace is zero. trace is also equal to sum of eigenvalues, hence two eigenvalues must be iota and other two must be -iota.
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imaginary**
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read this comment if you got stuck anywhere.
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then ask further doubts if exist.
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ok
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Dhairya sharma

when we will find out the eigen value of the matrix..... multiply it by simply pi/2
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because it will aatisfy the matrix
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Abhishek singh

A complete solution to your doubt.
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do ask doubts if any
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before asking dubts, do read my other comments first. I have explained almost everything
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if you got stuck anywhere, do ask.
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Dhairya sharma

dear, we can find out it's eigen value directly...... don't go tough method....... it's 4×4 matrix....we can solve it by this method see attached
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i hope u get it dear
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eigen value of anti hermitian or skew hermitian is always imaginary.
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Dhairya sharma

just like previous one evry matrix satify by its eigen value if we multiply it both side by k it won't effect
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trace is sum of the eigen value
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dear see attached
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since it's skew hermitian matrix.
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i don't know what is hermitian matrix
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matrix which satisfies a(degger) = a is hermitian
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when u go further in matrix u will get to know what it is
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