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The eigenvalue of a symmetric matrix are all;
  • a)
    Complex with non-zero positive imaginary part
  • b)
    Complex with non-zero negative imaginary part
  • c)
    Real
  • d)
    Pure imaginary
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The eigenvalue of a symmetric matrix are all;a)Complex with non-zero ...
Consider a symmetric matrix
The characteristic equation for this matrix is |M-λI| = 0
a - λ = ±b
∴ λ = a±b is a real value
Therefore, for a real symmetric matrix eigen values are real.
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The eigenvalue of a symmetric matrix are all;a)Complex with non-zero positive imaginary partb)Complex with non-zero negative imaginary partc)Reald)Pure imaginaryCorrect answer is option 'C'. Can you explain this answer?
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