Operator r is a diagonal matrix in position representation

1. Jan 27, 2016

Happiness

What does it mean by "In the position representation -- in which r is diagonal" in the paragraph below? How can we show that?

Does it mean equation (3) in http://scienceworld.wolfram.com/physics/PositionOperator.html? (where I believe the matrix is in the $|E_n>$ basis)

2. Jan 27, 2016

blue_leaf77

The matrix element of position operator $\hat{\mathbf{r}}$ in position representation reads as
$$\langle \mathbf{r'} | \hat{\mathbf{r}} | \mathbf{r''} \rangle= \mathbf{r'} \delta(\mathbf{r'}-\mathbf{r''})$$
which vanishes for off-diagonal elements.