Diagonal matrix: Difference between revisions

Revision as of 23:16, 23 March 2025

Revision as of 23:17, 23 March 2025

Line 65:

==Matrix-to-vector diag operator==

The inverse matrix-to-vector {{math|diag}} operator is sometimes denoted by the identically named <math>\operatorname{diag}(\mathbf{D}) = \begin{bmatrix}a_1 & \dotsmdots & a_n\end{bmatrix}^\textsf{T},</math> where the argument is now a matrix, and the result is a vector of its diagonal entries.

The following property holds:

<math display="block">
\operatorname{diag}(\mathbf{A}\mathbf{B}) = \sum_j \left(\mathbf{A} \circ \mathbf{B}^\textsf{T}\right)_{ij} = \left( \mathbf{A} \circ \mathbf{B}^\textsf{T} \right) \mathbf{1} .
</math>

== Scalar matrix ==