How to multiply a matrix with a quaternion

Hi, I got a problem while performing image encryption using quaternions. In that, I need to perform a multiplication q.B.(q^-1) where q is a quaternion and q^-1 is quaternion inverse and B is a square matrix of size 363X363. How to perform this multiplication using matlab? Moreover I need to repeat this multiplication in a for loop. Awaiting your suggestions. Thank you in advance.

[James Tursa]

The operation you describe isn't defined. First, the formulation as you have written it q.B.(q^-1) leads me to believe that the . multiply is a quaternion multiply and not a matrix multiply. I.e., you intend this to be a rotation of B. But for this to make sense to me, B would need to be a quaternion or a vector, not a large matrix. So I am confused as to what you want. Can you elaborate?