Description Usage Arguments Details Author(s) See Also Examples
View source: R/linearAlgebra-pinv_of_dcap.R
The Moore-Penrose inverse of the duplication matrix.
1 | pinv_of_dcap(k)
|
k |
Positive integer.
Dimension of the |
The Moore-Penrose inverse of the duplication matrix \mathbf{D}_{k} is the \frac{1}{2} k ≤ft( k + 1 \right) \times k^2 matrix given by
\mathbf{D}_{k}^{+} = ≤ft( \mathbf{D}_{k}^{\prime} \mathbf{D}_{k} \right)^{-1} \mathbf{D}_{k}^{\prime}
where
\mathbf{D}_{k}^{+} \mathrm{vec} ≤ft( A \right) = \mathrm{vech} ≤ft( \mathbf{A} \right) \quad ≤ft( \mathbf{A} = \mathbf{A}^{\prime} \right)
\mathrm{vec} ≤ft( \cdot \right) is the vectorization of a matrix, and \mathrm{vech} ≤ft( \cdot \right) is the half-vectorization of a matrix.
Ivan Jacob Agaloos Pesigan
Other Symmetric Functions:
dcap()
,
mcap_cor()
,
mcap_diag()
,
mcap_sym()
,
sym_of_vechs()
,
sym_of_vech()
1 | pinv_of_dcap(3)
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