GATE 2026 EE – Question 35
$A$ is an $m\times m$ skew-symmetric matrix with real-valued entries, and $\boldsymbol x$ is an $m$-dimensional column vector with real-valued entries such that $\boldsymbol x^T\boldsymbol x=1$. The quantity $\boldsymbol x^TA\boldsymbol x$ evaluates to ______.
(Answer in integer)
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Correct answer: 0
Explanation
$\boldsymbol x^TA\boldsymbol x$ is a scalar, so it equals its transpose: $\boldsymbol x^TA\boldsymbol x=(\boldsymbol x^TA\boldsymbol x)^T=\boldsymbol x^TA^T\boldsymbol x=-\boldsymbol x^TA\boldsymbol x$. Hence $2\boldsymbol x^TA\boldsymbol x=0$ and the value is 0.