Editing Diagonal matrix (section)

==Vector-to-matrix diag operator==

A diagonal matrix {{math|'''D'''}} can be constructed from a vector <math>\mathbf{a} = \begin{bmatrix}a_1 & \dots & a_n\end{bmatrix}^\textsf{T}</math> using the <math>\operatorname{diag}</math> operator:
<math display="block">
 \mathbf{D} = \operatorname{diag}(a_1, \dots, a_n).
</math>

This may be written more compactly as <math>\mathbf{D} = \operatorname{diag}(\mathbf{a})</math>.

The same operator is also used to represent [[Block matrix#Block diagonal matrices|block diagonal matrices]] as <math>\mathbf{A} = \operatorname{diag}(\mathbf A_1, \dots, \mathbf A_n)</math> where each argument {{math|'''A'''{{sub|''i''}}}} is a matrix.

The {{math|diag}} operator may be written as
<math display="block">
 \operatorname{diag}(\mathbf{a}) = \left(\mathbf{a} \mathbf{1}^\textsf{T}\right) \circ \mathbf{I},
</math>
where <math>\circ</math> represents the [[Hadamard product (matrices)|Hadamard product]], and {{math|'''1'''}} is a constant vector with elements 1.