Gate

A quantum gate is a (typically unitary) operation applied to one or more qubits, represented by a matrix.

A gate is the basic building block of quantum circuits.

Example (Hadamard)

H = \tfrac{1}{\sqrt{2}}\begin{pmatrix}1 & 1\\1 & -1\end{pmatrix}.

Applying $H$ to $|0\rangle$ creates a superposition.