Duplication and elimination matrices

In mathematics, especially in linear algebra and matrix theory, the duplication matrix and the elimination matrix are linear transformations used for transforming half-vectorizations of matrices into vectorizations or (respectively) vice versa. == Duplication matrix == The duplication matrix D n {\displaystyle D_{n}} is the unique n 2 × n ( n + 1 ) 2 {\displaystyle n^{2}\times {\frac {n(n+1)}{2}}} matrix which, for any n × n {\displaystyle n\times n} symmetric matrix A {\displaystyle A} , transforms v e c h ( A ) {\displaystyle \mathrm {vech} (A)} into v e c ( A ) {\displaystyle \mathrm {vec} (A)} : D n v e c h ( A ) = v e c ( A ) {\displaystyle D_{n}\mathrm {vech} (A)=\mathrm {vec} (A)} .

Source: Wikipedia — Duplication and elimination matrices (CC BY-SA 4.0)

Duplication and elimination matrices

In mathematics, especially in linear algebra and matrix theory, the duplication matrix and the elimination matrix are linear transformations used for transforming half-vectorizations of matrices into vectorizations or (respectively) vice versa. == Duplication matrix == The duplication matrix D n {\displaystyle D_{n}} is the unique n 2 × n ( n + 1 ) 2 {\displaystyle n^{2}\times {\frac {n(n+1)}{2}}} matrix which, for any n × n {\displaystyle n\times n} symmetric matrix A {\displaystyle A} , transforms v e c h ( A ) {\displaystyle \mathrm {vech} (A)} into v e c ( A ) {\displaystyle \mathrm {vec} (A)} : D n v e c h ( A ) = v e c ( A ) {\displaystyle D_{n}\mathrm {vech} (A)=\mathrm {vec} (A)} .

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Source: Wikipedia "Duplication and elimination matrices" · CC BY-SA 4.0

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