Diagonal matrix: Difference between revisions

Revision as of 06:57, 26 February 2023

Revision as of 06:58, 26 February 2023

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==Matrix-to-vector diag operator==

The inverse matrix-to-vector <math>\operatorname{diag}</math> operator is sometimes denoted by the identically named <math>\operatorname{diag}(\mathbf{D}) = \begin{bmatrix}a_1 & \dotsm & 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}(AB\mathbf{A}\mathbf{B}) = \sum_j \left(\mathbf{A} \circ \mathbf{B}^\textsf{T}\right)_{ij} </math>

== Scalar matrix ==