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The high-resolution algorithms of array processing assume that the matrix is diagonal with constant element.
For the white noise case, the noise covariance matrix is diagonal, i.e.e.e
The data errors are assumed to be uncorrelated so the weight matrix is diagonal.
Since the matrix is diagonal, (16) can be decomposed into a set of scalar equations (17).
The modified system matrix is diagonal, with the elements given in (19).
This process is equivalent to finding the axis system in which the covariance matrix is diagonal.
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In this paper, we proved that isolation is optimal if the fault response matrix and noise covariance matrix are diagonal simultaneously.
Usually the noise matrices are diagonal matrices.
Therefore, for simplicity, we have assumed that these matrices are diagonal.
Moreover, the mass matrices are diagonal, thus time marching is explicit and is very efficient.
Although the discretization matrices usually are sparse, their exponentials are not, unless the discretization matrices are diagonal.
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