qkn_coeffr function

Coefficient Matrix $\tilde{C}_k$

This function computes the coefficient matrix for $\tilde{\mathcal{C}}_k$ for $W \sim W_m^{\beta}(n, \Sigma)$.

qkn_coeffr(k, alpha = 2)

Arguments

• k: The order of the $\tilde{\mathcal{C}}_k$ matrix (a positive integer)

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

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

Returns

A list with two elements:

• c: A 3-dimensional array containing the coefficient matrices of the numerator of $\tilde{\mathcal{C}}_k$ in descending powers of $n1$, where $n1 = n - m + 1 - \alpha$.
• den: A vector containing the coefficients of the denominator of $\tilde{\mathcal{C}}_k$, in descending powers of $n1$.

Examples

# Example 1:
qkn_coeffr(2) # For real Wishart distribution with k = 2

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

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