Conjugate symmetry is a property of inner product spaces that states for any two vectors, the inner product of one vector with the conjugate of the other is equal to the complex conjugate of the inner product of the second vector with the first. This means that if you take the inner product of vectors \( u \) and \( v \), it holds that \( \langle u, v \rangle = \overline{\langle v, u \rangle} \). This concept is essential in defining norms and distances in complex vector spaces.
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