wish_ps function

Coefficient Matrix $\mathcal{H}_k$

This function computes the coefficient matrix $\mathcal{H}_k$ that allows us to compute the expected value of a power-sum symmetric function of $W$, where $W \sim W_m^{\beta}(n,\Sigma)$.

wish_ps(k, alpha = 2)

Arguments

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

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

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

Returns

A coefficient matrix $\mathcal{H}_k$ that allows us to compute the expected value of a power-sum symmetric function of $W$, where $W \sim W_m^{\beta}(n,\Sigma)$. 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 $n$.

Examples

# Example 1:
wish_ps(3) # For real Wishart distribution with k = 3

# Example 2:
wish_ps(4, 1) # For complex Wishart distribution with k = 4

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