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Once elements are separated, the stiffness matrix becomes singular.

However, it may suffer the convergence issue when the system is under the stressed condition and the Jacobian matrix becomes singular.

When this is not the case, the performance of the GLRT degenerates because the sample covariance matrix becomes singular, and the whole problem becomes ill-conditioned [16, 17].

Conventional power flow methods like Newton Raphson, Gauss Siedel, fast decoupled power flow methods suffer to provide proper MLL under security constraints as Jacobian matrix becomes singular when system loading approaches its loadability limit.

In such situation the common Mahalanobis distance, used in the previous papers, is computationally expensive to be used for the parameters estimation, since the sample covariance matrix becomes singular in presence of small samples.

Although the Galerkin matrix becomes singular for (varepsilon=0) we can in principle still solve the linear system if it is consistent, i.e. if the right-hand side lies in the range of the Galerkin matrix.

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This is because the essential reason leads to the voltage collapse of an integrated power system is the load increase of the distribution grid and the Jacobin matrix of integrated system becomes singular due to the singularity of the sub-matrix of the distribution grid, which cannot be reflected in the traditional independent transmission CPF.

Since the computation of 's from (24) involves an inverse operation on a matrix (one-time job), it may not be computable when the matrix becomes (near) singular, which occurs when the channel is very slow fading.

When, which means that the brightness ratio in the green and in the red channel is the same for both dyes, matrix M in Equation (26a) becomes singular and is not invertible.

In previous papers, this failure has been attributed to ill-conditioning problems which prevail as the singularity is approached, but issues such as whether the coefficient matrix will become singular or whether one will obtain good results when the effects of ill-conditioning can be annihilated have not been discussed.

Then the natural frequencies of vibrations are found as the frequencies that cause this matrix to become singular.

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