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Let A be an n x n complex matrix. Assume that A is self-adjoint and let B denotes the inverse of (A + iIn). Then all eigenvalues of (A - iIn)B are 
  • a)
    purely imaginary
  • b)
    of modulus one
  • c)
    real
  • d)
    of modulus less than one
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let A be an n x n complex matrix. Assume that A is self-adjoint and le...

  • Self-adjoint Matrix: A self-adjoint (Hermitian) matrix A has real eigenvalues.
  • Matrix B: B is the inverse of (A - iIn).
  • Eigenvalues of (A - iIn)B:

    • (A - iIn)B is the identity matrix, as B is the inverse of (A - iIn).
    • The eigenvalues of the identity matrix are 1.

    •  
  • Conclusion: All eigenvalues of (A - iIn)B have modulus one, making option B correct.

  •  
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Let A be an n x n complex matrix. Assume that A is self-adjoint and let B denotes the inverse of (A + iIn). Then all eigenvalues of (A - iIn)B area)purely imaginaryb)of modulus onec)reald)of modulus less than oneCorrect answer is option 'B'. Can you explain this answer?
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Let A be an n x n complex matrix. Assume that A is self-adjoint and let B denotes the inverse of (A + iIn). Then all eigenvalues of (A - iIn)B area)purely imaginaryb)of modulus onec)reald)of modulus less than oneCorrect answer is option 'B'. Can you explain this answer? for Engineering Mathematics 2025 is part of Engineering Mathematics preparation. The Question and answers have been prepared according to the Engineering Mathematics exam syllabus. Information about Let A be an n x n complex matrix. Assume that A is self-adjoint and let B denotes the inverse of (A + iIn). Then all eigenvalues of (A - iIn)B area)purely imaginaryb)of modulus onec)reald)of modulus less than oneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Engineering Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A be an n x n complex matrix. Assume that A is self-adjoint and let B denotes the inverse of (A + iIn). Then all eigenvalues of (A - iIn)B area)purely imaginaryb)of modulus onec)reald)of modulus less than oneCorrect answer is option 'B'. Can you explain this answer?.
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