Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > Matrix R is :a)Positive semi definite symmetr... Start Learning for Free
Matrix R 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 R is :a)Positive semi definite symmetric matrixb)Positive defin...
Explanation: Matrix R 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 R is :a)Positive semi definite symmetric matrixb)Positive defin...
Positive semi-definite symmetric matrix:
A matrix R is said to be positive semi-definite if all of its eigenvalues are non-negative. In addition, R is said to be symmetric if it is equal to its transpose.
Explanation:
To determine if the given matrix R is positive semi-definite and symmetric, we need to check two conditions:
1. Symmetric Property:
To check if the matrix is symmetric, we compare it with its transpose. If they are equal, then the matrix is symmetric. Mathematically, if R = R^T, where R^T denotes the transpose of matrix R, then the matrix R is symmetric.
2. Positive Semi-definite Property:
To check if the matrix is positive semi-definite, we need to find all the eigenvalues of the matrix and check if they are non-negative.
If both conditions are satisfied, then the matrix R is positive semi-definite symmetric.
Conclusion:
Based on the given options, the correct answer is option 'A' - Positive semi-definite symmetric matrix.
A matrix R is said to be positive semi-definite if all of its eigenvalues are non-negative. In addition, R is said to be symmetric if it is equal to its transpose.
Explanation:
To determine if the given matrix R is positive semi-definite and symmetric, we need to check two conditions:
1. Symmetric Property:
To check if the matrix is symmetric, we compare it with its transpose. If they are equal, then the matrix is symmetric. Mathematically, if R = R^T, where R^T denotes the transpose of matrix R, then the matrix R is symmetric.
2. Positive Semi-definite Property:
To check if the matrix is positive semi-definite, we need to find all the eigenvalues of the matrix and check if they are non-negative.
If both conditions are satisfied, then the matrix R is positive semi-definite symmetric.
Conclusion:
Based on the given options, the correct answer is option 'A' - Positive semi-definite symmetric matrix.
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