In some particular cases, the genericity is satisfied by providing a channel matrix with random and independent coefficients.
Finding the rank of a matrix with random elements is quite challenging and requires a very involved derivation.
where H is the N r ×N t channel matrix with random entries h k ℓ denoting the gain of the radio channel between the ℓth transmitting antenna and the kth receiving antenna.
From the micrographs of the samples heat treated at 525°C and 550°C, the KNN crystals were rectangular in shape and were embedded in the glass matrix with random orientations.
where A is an m × m matrix with random elements, B is an m-dimensional column vector function whose elements are random variables, φ : Ω → R m, φ ∈ C , ξ ( t ) is a random Markov process with a finite number of states θ k, k = 1, 2, …, q, the probabilities of which are p k ( t ) = P { ξ ( t ) = θ k }, k = 1, 2, …, q, (3).
where A is an m × m matrix with random elements, B is an m-dimensional column vector with random elements, ξ n is the Markov chain of a finite number of states θ 1, θ 2, …, θ q with probabilities p k ( n ) = P { ξ n = θ k }, k = 1, 2, …, q, n = 1, 2, … , that satisfy the system of difference equations p ( n + 1 ) = Π p ( n ), (3).
