Matrix algebra over a field

Conjugate transpose

The conjugate transpose or Hermitian conjugate 𝐴† of a complex matrix 𝐴 is the Matrix transpose 𝐴𝖳 with complex conjugate entries. linalg Thus if 𝐴 =(𝑎𝑖𝑗) then 𝐴† =(―――𝑎𝑗𝑖). The conjugate transpose is an important manifestation of Duality: If vectors in a complex vector space ℂ𝑛 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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