mcap_sym: The Symmetric Pattern Matrix
In jeksterslab/linearAlgebra: Linear Algebra with R

Description Usage Arguments Details Value Author(s) References See Also Examples

Creates a symmetric pattern matrix.

1	mcap_sym(k)

`k`	Positive integer. Dimension of the `k` by `k` matrix.

\mathbf{M}_{k} ≤ft( s \right) is the k \times k symmetric pattern matrix with

≤ft( \mathbf{M}_{k} ≤ft( s \right) \right)_{ij, gh} = \begin{cases} 1 & \text{if} \quad i = j = g = h , \\ \frac{1}{2} & \text{if} \quad ≤ft( i, j \right) = ≤ft( g, h \right) \text{or} ≤ft( i, j \right) = ≤ft( h, g \right) , \\ 0 & \text{otherwise} . \end{cases}

A matrix.

Ivan Jacob Agaloos Pesigan

Nel, D. G. (1985). A matrix derivation of the asymptotic covariance matrix of sample correlation coefficients. Linear Algebra and its Applications, 67, 137–145. https://doi.org/10.1016/0024-3795(85)90191-0

Other Symmetric Functions: dcap(), mcap_cor(), mcap_diag(), pinv_of_dcap(), sym_of_vechs(), sym_of_vech()