The DiagonalMatrix(V) command constructs a (block) diagonal Matrix whose diagonal entries, starting from the upper-left corner, are the elements of V.

If V is a Vector or a list of scalar values, then the blocks are $1x1$ and DiagonalMatrix(V) constructs a diagonal Matrix.

If V is a list $\left[\mathrm{B1}\,\mathrm{B2}\,\dots \,\mathrm{Bn}\right]$ containing any non-scalar value, then the blocks are not necessarily $1x1$ and DiagonalMatrix(V) builds a Matrix by placing each element, Bj, of V as an expanded block of entries, with each block placed immediately below and to the right of its predecessor. If the elements of V are all square (scalar values or square Matrices), a diagonal or block diagonal Matrix in the usual sense is returned.

By using this command in conjunction with the JordanBlockMatrix command, you can create a Jordan Matrix.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\:$

$L≔\left[⟨⟨1\,2⟩|⟨x\,y⟩⟩\,3\,⟨⟨4\,5⟩|⟨6\,7⟩⟩\right]$

$L≔\left[\left[\begin{array}{cc}1& x\\ 2& y\end{array}\right]\,3\,\left[\begin{array}{cc}4& 6\\ 5& 7\end{array}\right]\right]$

$\mathrm{DiagonalMatrix}\left(L\right)$

$\left[\begin{array}{ccccc}1& x& 0& 0& 0\\ 2& y& 0& 0& 0\\ 0& 0& 3& 0& 0\\ 0& 0& 0& 4& 6\\ 0& 0& 0& 5& 7\end{array}\right]$

$V≔⟨1\,2\,3\,4⟩$

$V≔\left[\begin{array}{c}1\\ 2\\ 3\\ 4\end{array}\right]$

$\mathrm{DiagonalMatrix}\left(V\right)$

$\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 2& 0& 0\\ 0& 0& 3& 0\\ 0& 0& 0& 4\end{array}\right]$