dkmap function

Mapping Matrix that maps $Q_{k+1}$ to $Q_k$ for a beta-Wishart Distribution, but without $n$ on the diagonal

This function computes the matrix that maps $Q_{k+1}$ to $Q_k$ when $W \sim W_m^{\beta}(n, \Sigma)$.

dkmap(k, alpha = 2)

Arguments

• k: The order of the mapping matrix $D_k$ (a positive integer)

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

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

Returns

A matrix that maps $Q_{k+1}$ to $Q_k$, but without $n$ on the diagonal.

Examples

# Example 1: Compute the mapping matrix for k = 2, real Wishart
dkmap(2)
# Example 2: Compute the mapping matrix for k = 1, complex Wishart
dkmap(1, 1)
# Example 3: Compute the mapping matrix for k = 2, quaternion Wishart
dkmap(2, 1/2)