qkn_coeff function

Inverse of a Coefficient Matrix $\tilde{\mathcal{C}}_k$

This function computes the inverse of the coefficient matrix $\tilde{\mathcal{C}}_k$

qkn_coeff(k, alpha = 2)

Arguments

• k: The order of the $\tilde{\mathcal{C}}_k$ matrix

• alpha: The type of beta-Wishart distribution ($\alpha=2/\beta$):

  • 1/2: Quaternion Wishart
  • 1: Complex Wishart
  • 2: Real Wishart (default)

Returns

Inverse of a coefficient matrix $\tilde{\mathcal{C}}_k$ that allows us to obtain $E[p_{\lambda}(W^{-1})W^{-r}]$, where $r+|\lambda|=k$

and $W ~ W_m^{\beta}(n,\Sigma)$. The matrix is represented as a 3-dimensional array where each slice along the third dimension represents a coefficient matrix of the polynomial in descending powers of $\tilde{n}$.

Examples

# Example 1:
qkn_coeff(2) # For real Wishart distribution with k = 2
# Example 2:
qkn_coeff(3, 1) # For complex Wishart distribution with k = 3

# Example 3:
qkn_coeff(2, 1/2) # For quaternion Wishart distribution with k = 2