Mathematics Exam > Mathematics Questions > Which of the following(s) is/are correct?a)Th...
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Which of the following(s) is/are correct?
- a)The eigen values of a real symmetric matrix are all real
- b)The modulus of each eigen value of a unitary matrix is unity
- c)The eigen value of a Skew — Hermitian Matrix is either zero or a pure imaginary number
- d)None of these
Correct answer is option 'A,B,C'. Can you explain this answer?
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Which of the following(s) is/are correct?a)The eigen values of a real ...
A) The eigenvalues of a real symmetric matrix are all real. This statement is correct. It is a known property of real symmetric matrices that their eigenvalues are always real.
b) The modulus of each eigen value of a unitary matrix is unity. This statement is correct. A unitary matrix is defined as a square matrix whose conjugate transpose is its inverse. The eigenvalues of a unitary matrix lie on the unit circle in the complex plane, which means their modulus is always unity.
c) The eigenvalue of a Skew-symmetric matrix is always zero. This statement is incorrect. A skew-symmetric matrix is a square matrix whose transpose is equal to the negation of itself. The eigenvalues of a skew-symmetric matrix can be either zero or purely imaginary (non-zero).
b) The modulus of each eigen value of a unitary matrix is unity. This statement is correct. A unitary matrix is defined as a square matrix whose conjugate transpose is its inverse. The eigenvalues of a unitary matrix lie on the unit circle in the complex plane, which means their modulus is always unity.
c) The eigenvalue of a Skew-symmetric matrix is always zero. This statement is incorrect. A skew-symmetric matrix is a square matrix whose transpose is equal to the negation of itself. The eigenvalues of a skew-symmetric matrix can be either zero or purely imaginary (non-zero).
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Which of the following(s) is/are correct?a)The eigen values of a real symmetric matrix are all realb)The modulus of each eigen value of a unitary matrix is unityc)The eigen value of a Skew — Hermitian Matrix is either zero or a pure imaginary numberd)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer?
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Which of the following(s) is/are correct?a)The eigen values of a real symmetric matrix are all realb)The modulus of each eigen value of a unitary matrix is unityc)The eigen value of a Skew — Hermitian Matrix is either zero or a pure imaginary numberd)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which of the following(s) is/are correct?a)The eigen values of a real symmetric matrix are all realb)The modulus of each eigen value of a unitary matrix is unityc)The eigen value of a Skew — Hermitian Matrix is either zero or a pure imaginary numberd)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following(s) is/are correct?a)The eigen values of a real symmetric matrix are all realb)The modulus of each eigen value of a unitary matrix is unityc)The eigen value of a Skew — Hermitian Matrix is either zero or a pure imaginary numberd)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer?.
Which of the following(s) is/are correct?a)The eigen values of a real symmetric matrix are all realb)The modulus of each eigen value of a unitary matrix is unityc)The eigen value of a Skew — Hermitian Matrix is either zero or a pure imaginary numberd)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which of the following(s) is/are correct?a)The eigen values of a real symmetric matrix are all realb)The modulus of each eigen value of a unitary matrix is unityc)The eigen value of a Skew — Hermitian Matrix is either zero or a pure imaginary numberd)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following(s) is/are correct?a)The eigen values of a real symmetric matrix are all realb)The modulus of each eigen value of a unitary matrix is unityc)The eigen value of a Skew — Hermitian Matrix is either zero or a pure imaginary numberd)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer?.
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