augmented matrix


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augmented matrix

[′ȯg·men·təd ′mā·triks]
(mathematics)
The matrix of the coefficients, together with the constant terms, in a system of linear equations.
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It is implied that the fusion center needs the augmented matrix computation ability.
According to the knowledge of linear algebra, the equations exit nontrivial solution if the rank of coefficient matrix is equal to the rank of the augmented matrix as below.
We denote by [??] = [A B] [member of] [R.sup.mx(n+k)] the augmented matrix of (3); this is the matrix obtained from A by adding matrix B.
If the rank of B's is the same as that of the augmented matrix (B's|y), B'sa' = y is a consistent equation, and there exist infinite solution a'=[B'.sup.-.sub.s] y + (I-[B'.sup.-.sub.s][B'.sub.s])d that satisfy B'sa'=y, where [B'.sup.-.sub.s] is the matrix 1-inverse of B's and d is an arbitrary nonzero vector of length k [Mayer 2001].
The augmented matrix [S.sub.m] := [U [V.sub.m]] contains as columns the basis for U and [K.sub.m] ([PA.sub.p], [r.sub.0]).
DKPCA fault diagnosis method is that each of the observation variables is expanded by H observations in front, the augmented matrix containing the first S time observations is constructed [12], and augmented matrix is as follows:
After many trials augmented matrix of size M x N, given by equation (3), formed by combining identity matrix of size M x M, and zero matrix of size M x (N - M), was found to extract necessary information selectively since it has unity values in the leading diagonal.
The augmented matrix equation expressed in generalized coordinates is
Note that received transfer units containing coefficient vectors and coded data blocks should be organized as an augmented matrix in which a transfer unit constitutes a row such that the progressive decoding/GE can be run on the matrix.
The responses of the circuits computed by means of MATLAB and the standard ordinary differential equation (ODE) integration routines are assumed as the reference curves in this study.The reference curves are compared with the solution obtained by means of the linear inversion of the augmented matrix equation like (29).
To obtain the solution of (1) under conditions (2), by replacing the rows in matrix (39) by the last m rows of matrix (41), we have the required augmented matrix

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