I read about Hadamard gate H and found it's matrix representation as follows:
$$H_1=\frac{1}{\sqrt 2}\begin{pmatrix}1 & 1 \\1 & -1\end{pmatrix}$$
I wanted to know what will be the matrix representation of H in computational basis.
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Sign up to join this communityI read about Hadamard gate H and found it's matrix representation as follows:
$$H_1=\frac{1}{\sqrt 2}\begin{pmatrix}1 & 1 \\1 & -1\end{pmatrix}$$
I wanted to know what will be the matrix representation of H in computational basis.
This is the matrix representation of $H$ in the computational basis. The first column is the image of $|0\rangle$ and the second column is the image of $|1\rangle$.
The reason that $H$ looks the same in both the computational and the "plus/minus" basis is that $H$ is a self-adjoint (or hermitian) unitary, this makes it very special as it means that its self-inverse since we have that $$H^{−1}=H^\dagger=H\,.$$