Conjugate transpose

The conjugate transpose or Hermitian conjugate $𝐴 †$ of a complex matrix $𝐴$ is the Matrix transpose $𝐴 𝖳$ with complex conjugate entries. #m/def/linalg Thus if $𝐴 = (𝑎 𝑖 𝑗)$ then $𝐴 † = (――― 𝑎 𝑗 𝑖)$ . The conjugate transpose is an important manifestation of Duality: If vectors in a complex vector space $ℂ 𝑛$ are represented as column vectors, the Dual space is that of row vectors and the duals of linear maps and vectors with respect to the standard inner product is given by the conjugate transpose.

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