denpoly function

Coefficients of the Denominator Polynomial for $\tilde{H}_k$ and $\tilde{C}_k$

This function computes the coefficients of the denominator polynomial for the elements of $\tilde{H}_k$ and $\tilde{C}_k$. The function returns a vector containing the coefficients in descending powers of $\tilde{n}$, with the last element being the coefficient of $\tilde{n}$.

denpoly(k, alpha = 2)

Arguments

• k: The order of the polynomial (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 vector containing the coefficients of the denominator polynomial in descending powers of $\tilde{n}$ for the elements of $\tilde{H}_k$ and $\mathcal{C}_k$.

Examples

# Example 1: Compute the denominator polynomial for k = 3, alpha = 2
# Output corresponds to the polynomial n1^5-3n1^4-8n1^3+12n1^2+16n1,
# where n1 is \eqn{\tilde{n}}
denpoly(3)

# Example 2: Compute the denominator polynomial for k = 2, alpha = 1
# Output corresponds to the polynomial n1^3-n1, where n1 is \eqn{\tilde{n}}
denpoly(2, alpha = 1)