Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > Matrix Q is :a)Positive semi definite symmetr...
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Matrix Q is :
- a)Positive semi definite symmetric matrix
- b)Positive definite non-symmetric matrix
- c)Negative definite symmetric matrix
- d)Negative definite non-symmetric matrix
Correct answer is option 'A'. Can you explain this answer?
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Matrix Q is :a)Positive semi definite symmetric matrixb)Positive defin...
Explanation: Matrix Q defines positive definite or non-definite symmetric matrix which is used in the performance index so as to give equal weightage to each element.
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Matrix Q is :a)Positive semi definite symmetric matrixb)Positive defin...
Positive semi definite symmetric matrix
A matrix is said to be positive semi-definite if it satisfies the following conditions:
1. It is symmetric.
2. All its eigenvalues are non-negative (greater than or equal to zero).
A. Positive semi-definite symmetric matrix
In this case, the matrix Q satisfies both conditions of positive semi-definite and is symmetric.
Explanation:
1. Symmetric Matrix
A matrix is symmetric if it is equal to its transpose. In other words, if Q is a symmetric matrix, then Q^T = Q.
2. Eigenvalues
Eigenvalues are scalar values associated with a matrix. For a given square matrix Q, the eigenvalues can be found by solving the equation Qv = λv, where v is the eigenvector and λ is the eigenvalue.
For a positive semi-definite matrix, all the eigenvalues should be greater than or equal to zero. In this case, matrix Q satisfies this condition.
Conclusion
Based on the given information, the matrix Q is a positive semi-definite symmetric matrix as it is symmetric and all its eigenvalues are non-negative.
Note: It is important to note that the given information does not provide any details about the size or specific elements of the matrix Q. The conclusion is based solely on the conditions for positive semi-definite symmetric matrices.
A matrix is said to be positive semi-definite if it satisfies the following conditions:
1. It is symmetric.
2. All its eigenvalues are non-negative (greater than or equal to zero).
A. Positive semi-definite symmetric matrix
In this case, the matrix Q satisfies both conditions of positive semi-definite and is symmetric.
Explanation:
1. Symmetric Matrix
A matrix is symmetric if it is equal to its transpose. In other words, if Q is a symmetric matrix, then Q^T = Q.
2. Eigenvalues
Eigenvalues are scalar values associated with a matrix. For a given square matrix Q, the eigenvalues can be found by solving the equation Qv = λv, where v is the eigenvector and λ is the eigenvalue.
For a positive semi-definite matrix, all the eigenvalues should be greater than or equal to zero. In this case, matrix Q satisfies this condition.
Conclusion
Based on the given information, the matrix Q is a positive semi-definite symmetric matrix as it is symmetric and all its eigenvalues are non-negative.
Note: It is important to note that the given information does not provide any details about the size or specific elements of the matrix Q. The conclusion is based solely on the conditions for positive semi-definite symmetric matrices.
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Matrix Q is :a)Positive semi definite symmetric matrixb)Positive definite non-symmetric matrixc)Negative definite symmetric matrixd)Negative definite non-symmetric matrixCorrect answer is option 'A'. Can you explain this answer?
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