Doubly stochastic processing on Jacket matrices

We proposed a novel method to generalize a set of 2" × 2" and 2n × 2n matrices named generalized doubly stochastic Jacket matrices, also orthostochastic cases are included. Generally, the proposed scheme uses a simple matrix factorization method to represent the doubly stochastic, Markov vectors and eigenvalues, and it can be easily applied for stochastic signal processing, Markov random process, Miller coding system, and orthogonal design for signal processing such as space time codes pattern design.