Given a natural number, the index of the multiplicative group of the-th powers of the non-zero elements of in } } is finite.
32.
So, to get linear independence all non zero m-tuples with one as a top most non zero element will be chosen as columns.
33.
In the Zbus, however, the impedance between two far away buses becomes very large, so there are no zero elements, making computation much harder.
34.
But, since the rationals are in fact a field, every non-zero element is a talk ) 16 : 20, 1 August 2014 ( UTC)
35.
In a field of field of any other characteristic, any non-zero element either has two square roots, as explained above, or does not have any.
36.
The general problem will have a rectangular array, probably with some zero elements . ?! talk ) 22 : 17, 27 October 2010 ( UTC)
37.
Unfortunately, applying Gaussian elimination ( or equivalently an LU decomposition ) to such a matrix results in the band being filled in by many non-zero elements.
38.
A structure which has a pair of non-zero elements, one of which is infinitesimal with respect to the other, is said to be "'non-Archimedean " '.
39.
However, it has a significant advantage in that each new zero element affects only the row with the element to be zeroed and the row above.
40.
Recall that the transvection : one such that all main diagonal elements are 1 and there is at most one non-zero element not on the diagonal.
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