The diag command either creates a matrix with entries on the diagonal, or extracts the entries from the diagonal of a matrix.

The diag(A) command returns a matrix with the entries of A along the main diagonal, and 0 everywhere else when A is a vector, or a matrix with one row or column.

The diag(A, k) command returns a matrix with the entries of A along the kth diagonal specified by the selection parameter k, and 0 everywhere else, when A is a vector, or a matrix with one row or column.

For a matrix A with more than one row and more than one column, the diag(A) command returns the main diagonal of A as a (column) vector.

For a matrix A with more than one row and more than one column, the diag(A, k) command returns the (column) vector corresponding to the diagonal of A, specified by the selection parameter k.

The diagonals of a matrix are indexed using signed integers, where the main diagonal has index 0. Superdiagonals are indexed with positive integers and subdiagonals are indexed with negative integers.

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,1\right]\,\left[4\,5\,6\right]\,\left[2\,8\,1\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 1\\ 4& 5& 6\\ 2& 8& 1\end{array}\right]$

$\mathrm{diag}\left(A\right)$

$\left[\begin{array}{c}1\\ 5\\ 1\end{array}\right]$

$\mathrm{diag}\left(A\,1\right)$

$\left[\begin{array}{c}2\\ 6\end{array}\right]$

$\mathrm{diag}\left(A\,-1\right)$

$\left[\begin{array}{c}4\\ 8\end{array}\right]$

$B≔\mathrm{Vector}\left(\left[4\,5\,6\right]\right)$

$B≔\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right]$

$\mathrm{diag}\left(B\right)$

$\left[\begin{array}{ccc}4& 0& 0\\ 0& 5& 0\\ 0& 0& 6\end{array}\right]$

$\mathrm{diag}\left(B\,1\right)$

$\left[\begin{array}{cccc}0& 4& 0& 0\\ 0& 0& 5& 0\\ 0& 0& 0& 6\\ 0& 0& 0& 0\end{array}\right]$

$\mathrm{diag}\left(B\,-1\right)$

$\left[\begin{array}{cccc}0& 0& 0& 0\\ 4& 0& 0& 0\\ 0& 5& 0& 0\\ 0& 0& 6& 0\end{array}\right]$