# What is the matrix representation of the Hadamard gate in the computational basis?

$$H_1=\frac{1}{\sqrt 2}\begin{pmatrix}1 & 1 \\1 & -1\end{pmatrix}$$

I wanted to know what will be the matrix representation of H in computational basis.

• Welcome on the QC SE! We have quite good Latex support here, but we don't really like screenshots. I don't know if your passes well this site, but if it is a border case, your chances are hugely increased by if you use Latex formulas. – peterh Sep 17 '20 at 15:11

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 $$H^{−1}=H^\dagger=H\,.$$
• It's just the matrix whose columns are the image of $H|+\rangle$ and $H|-\rangle$ – Condo Sep 17 '20 at 15:30