GATE EE 2015 Set 1 — Question 13
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Engineering Mathematics → Linear Algebra → Determinants
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Question
If the sum of the diagonal elements of a matrix is , then the maximum possible value of determinant of the matrix is ________.
Correct answer
9 to 9
Solution
Let the matrix be with , and let its eigenvalues be . ThenThe intended setting is a matrix with real eigenvalues (for example a real symmetric matrix). Then giveswith equality when , e.g. .(Without that restriction the determinant has no upper bound: has trace and determinant , with complex eigenvalues. The accepted value therefore rests on the real-eigenvalue reading.)Maximum possible determinant .
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