Difficulties in Computing Ranks of Matrices (OverRanking) – Noise / Machine Rounding Errors

Computer machine rounding errors produce values that are close to zero, but are not zero, thus they increase the ranks of a matrix when they shouldn’t.

In order to solve this problem a threshold is determined so that the values become zero if they are below the threshold and thus enables the matrices to have correct values and thus enables the ranks to be true.

Another problem is noise that can occur by measurements received that are slightly noisy.

Here too, a threshold is determined so that the values are considered an additional rank only if they are above a threshold and thus enables the matrices to have correct values and thus enables the ranks to be true.