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The coset of $x$ acts as left multiplication by the matrix $X$, and the coset of $y$ acts as left multiplication by the matrix $Y$. This defines the scalar multiplication for the $R$-module structure on $\mathbb{C}^n$.

Conditions: $X, Y \in M_{n\times n}(\mathbb{C})$ satisfy $XY+YX=0$.; $R = \mathbb{C}\langle x,y\rangle / \langle xy+yx\rangle$.; $v \in \mathbb{C}^n$.

The coset of $x$ acts as left multiplication by the matrix $X$, and the coset of $y$ acts as left multiplication by the matrix $Y$. This defines the scalar multiplication for the $R$-module structure on $\mathbb{C}^n$.

Conditions: $X, Y \in M_{n\times n}(\mathbb{C})$ satisfy $XY+YX=0$.; $R = \mathbb{C}\langle x,y\rangle / \langle xy+yx\rangle$.; $v \in \mathbb{C}^n$.