can we decompose $\mathcal{A}$ of $\Bbb{R}^n$as an orthogonal transformation and a dilation?

can we decompose $\mathcal{A}$ of $\Bbb{R}^n$as an orthogonal
transformation and a dilation?

Problem
Any linear transformation of $\Bbb{R}^n$ is the composition of an
orthogonal transformation and a dilation along perpendicular
directions(with distinct coefficients)


for any linear transformation $\mathcal{A}$ of $\Bbb{R}^n$, assume its
correspond matrix is $A$,it can be decomposed as below $$A=UDW$$,where
$U,W$ is unitary matrices, $D$ is diagonal matrix. So any linear
transformation $\mathcal{A}$ is the composition of an orthogonal
transformation($W$) and a dilation($D$) along perpendicular directions and
an orthogonal transformation($U$). But I don't know how to decompose
$\mathcal{A}$ as an orthogonal transformation and a dilation along
perpendicular. Please Help me. thanks.