Usefulness of Why Eigenvectors Corresponding to Distinct Eigenvalues of Symmetric Matrix are Orthogonal I didn't find a pre-existing question relating to what I'm going to ask, so I apologize if this is a duplicate question for one I hadn't found:

Why is the property that eigenvalues corresponding to distinct eigenvectors of a real symmetric matrix are orthogonal useful if the eigenvectors were bundled into a matrix?

I know why it's true that they are orthongonal, and I know that there are exactly $n$ not necessarily distinct eigenvalues of a real $n\times n$ symmetric matrix. I'm not sure why the corresponding eigenvectors "bundled into a matrix" is useful. You'd have a matrix whose columns are orthogonal to each other, but beyond that what does that accomplish? 
The answer may be simple and I'm just missing something. Any help is greatly appreciated.

We often want to change basis from the standard basis to a basis of eigenvectors for a particular matrix. Suppose that $\beta = (v_1, \ldots, v_n)$ is an ordered basis of eigenvectors for a matrix $A$. If 
$$Q = \begin{bmatrix} v_1 & \cdots & v_n \end{bmatrix},
$$ then $Q^{-1}$ is the change of basis matrix from the standard basis to the basis $\beta$. If $Q$ is orthogonal, then $Q^{-1} = Q^T$, and so $Q^T$ is our change of basis matrix.   
