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Part of Qiskit: Intro to Linear Algebra

AΒ HermitianΒ matrix is a matrix is that is equivalent to its Conjugate Transpose denoted †\dagger, which means if you flip the signs of the imaginary components of the matrix, and then reflect these components over the top left diagonal, the resulting matrix will be the one you started with:

Οƒy=(0βˆ’iΒ i0)β€…β€ŠβŸΉβ€…β€ŠΟƒy†=(0βˆ’(i)Β βˆ’(βˆ’i)0)Β =(0βˆ’iΒ i0)=Οƒy\sigma_{y} = \begin{pmatrix} 0 & -i\ i & 0 \end{pmatrix} \implies \sigma_{y}^{\dagger} = \begin{pmatrix} 0 & -(i)\ -(-i) & 0 \end{pmatrix}\ = \begin{pmatrix} 0 & -i\ i & 0 \end{pmatrix} = \sigma_{y}

Referenced in

Qiskit: Intro to Linear Algebra