Exact(5)
Defining the matrix Laplacian by (4.7).
By defining the matrix W i for the i th sub-interval as W i = [ W kℓ i ], k = 0, …, N d − 1 and ℓ = 0, …, m i, (10).
Therefore, by defining the matrix P as mathbf{P}=mathbf{I}-mu left(Eleft{{mathbf{Z}}^T k)right}otimes mathbf{I}right -mu left(mathbf{I}right -mueft{{mathbf{Z}}^T(k)right}right)+{mu}^2left(Eleft{{mathbf{Z}}^T(k)otI}otimesthbf{Z}}^T(k)right}right) (31)wEleft{{mathbf{mathbf{P}phi (32).
By defining the matrix Φt = (HHH + ξtI -1 and applying the matrix inversion lemma to Equation (34), the MSE cost function given by Equation (33) is reduced to [13] MMS E t, VP = ξtI -1B ∑ n = 1 N B d H [ n ] Φ t d [ n ].
By pre- and postmultiplying the left-hand side matrix in the above inequality by the matrix, respectively, and defining the matrix,,,, and, If we set then, and, and it can be concluded that the above matrix inequality is equivalent to (3.21).
Similar(54)
For each define the matrix.
We define the matrix (2.9).
Define the matrix with components.
Let us define the matrix functions (6.8).
Now, define the matrix as follows: (38).
Başar and Altay defined the matrix which generalizes the matrix.
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