Operator r is a diagonal matrix in position representation

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

Screen Shot 2016-01-28 at 4.23.08 am.png


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

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blue_leaf77
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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.
 
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