I have a diagonal matrix ${\bf D}_{n \times n}$ and a rectangular matrix ${\bf B}_{m \times n}$ where $n \gg m$.
All but $m$ rows of ${\bf B}$ have non-zero elements. These $m$ rows have only six non-zero elements. (So that ${\bf B}$ has exactly $6m$ non-zero elements.)
I am working on a problem that requires the product ${\bf B D B}^T_{m x m}$ and in all my tests in symbolic algebra software this product is a symmetric tridiagonal matrix. Of course this is not a proof.
Is it possible to show that ${\bf B D B}^T$ is always a symmetric tridiagonal matrix? Or otherwise.