GATE | GATE CS Mock 2018 | Set 2 | Question 65

An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix A^T?

(A) 0.125
(B) 1.75
(C) 7
(D) None of the above

Answer: (B)

Explanation: Since A is orthogonal, AA^T = I, so A^{-1} = A^T.
Eigen values of A^{-1} or A^T = 1 ,\frac{1}{2} and \frac{1}{4}
The sum of eigen values of a matrix is equal to its trace.
So trace of A^T = 1.75

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