How can I indicate that empty elements of a matrix are zero? I have the following transition matrix in an academic conference paper:
$$\mathbf{P}=\begin{bmatrix}
1-p & p   &       &        &         &      \\ 
        & 1-p & p &        &         &      \\ 
        &         &       & \ddots &         &      \\ 
        &         &       &        & 1-p & p\\ 
        &         &       &        &         & 1
\end{bmatrix}$$
What is the best way to indicate that the empty elements are zero? I could also add a description in the body of the text. I considered something like "the off-diagonal elements are zero", but there are nonzero elements off of the diagonal so this wouldn't be entirely accurate. 
 A: *

*One simple way: mention $P$ is bidiagonal.

Let $\mathbf{P}$ be the $n\times n$ bidiagonal matrix
  $$\mathbf{P}=\begin{bmatrix}
1-p & p   &       &        &         &      \\ 
        & 1-p & p &        &         &      \\ 
        &         &       & \ddots &         &      \\ 
        &         &       &        & 1-p & p\\ 
        &         &       &        &         & 1
\end{bmatrix}$$


*Another: write it (semi) explicitly by adding a big zero to indicate blocks identically zero (this is quite standard).

Let $\mathbf{P}$ be the $n\times n$ matrix
  $$\mathbf{P}=\begin{bmatrix}
1-p & p   &       &        &         &      \\ 
        & 1-p & p &        &     \Large 0    &      \\ 
        &         &       & \ddots &         &      \\ 
        &    \Large 0     &       &        & 1-p & p\\ 
        &         &       &        &         & 1
\end{bmatrix}$$


*A third: combine both.

Let $\mathbf{P}$ be the $n\times n$ bidiagonal matrix
  $$\mathbf{P}=\begin{bmatrix}
1-p & p   &       &        &         &      \\ 
        & 1-p & p &        &     \Large 0    &      \\ 
        &         &       & \ddots &         &      \\ 
        &    \Large 0     &       &        & 1-p & p\\ 
        &         &       &        &         & 1
\end{bmatrix}$$

Note: to be even more specific, you can write "upper bidiagonal."
