IIT JAM & CSIR NET - Physical Sciences

Electromagnetic Theory & Radiation question bank (Classical Mechanics & Electrodynamics)

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Q1.
[Classical Mechanics & Electrodynamics Problem #1] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)
All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal
(B)
Eigenvalues must always be positive integers
(C)
The matrix cannot be diagonalized under any orthogonal transformation
(D)
All eigenvalues are pure imaginary
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Q2.
[Classical Mechanics & Electrodynamics Problem #3] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)
All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal
(B)
All eigenvalues are pure imaginary
(C)
Eigenvalues must always be positive integers
(D)
The matrix cannot be diagonalized under any orthogonal transformation
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