Example sentences of "unc [conj] [adv] on " in BNC.
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| 1 | The first row of the product gives unc and in view of this , the second row , excluding its first element , gives unc and so on . |
| 2 | Then f may now be written as the quadratic form of which the matrix is the leading minor of A of order b — 1 , and we may deduce , corresponding to ( 22 ) , unc Now , by putting unc we establish a similar result for unc and so on , so that finally we establish that unc From ( 21 ) it is clear that a necessary and sufficient condition that f shall be positive is that Di shall be positive , all i . |
| 3 | Now it is possible to write down a sequence of matrices unc Mr ( r is usually n or n + 1 , depending on the variant employed ) which when used as a chain to premultiply A , condense it to the unit matrix , so that unc which evidently implies unc The numerical procedure is to operate successively on 91 ) ; given A we can write down M1 and we evaluate unc so that ( 1 ) becomes unc Knowing B we can now write down unc and form unc and so on , until R is obtained . |
| 4 | What we have done is to keep unc but use it to eliminate the leading elements of unc and so on , reducing the number of rows by 1 at each step . |
| 5 | unc and further steps give unc and so on . |
| 6 | For example , we may write it as unc and use the regression formula unc so that , for example , if Ro = 0 , we should obtain unc and so on . |
| 7 | Let unc Then , if we retain eight decimal places unc Hence , if unc and so on , we find as successive approximations to unc correct to six decimal places , |
| 8 | Next unc and so on . |
| 9 | As before , this may be developed in either of two ways , provided unc as r increases : x = q + Fx , suggesting the regression formula unc or unc Though the computations may be different , these two formulae are equivalent ; for if xo = 0 the regression formula gives unc and so on . |
| 10 | Then a computer will rapidly evaluate the successive products unc and so on . |
| 11 | In these methods , we apply a succession of similar transformations to a matrix A : unc and so on , until A is transformed into a form giving the eigenvalues directly : it may be a triangular form , or the ultimate canonical form unc ( or unc if A is defective ) . |
| 12 | When this element becomes very small unc tends to decrease by the factor unc and unc by unc and so on . |
| 13 | From the second column unc which yield in succession unc and so on . |
| 14 | However , here we do not resolve A into unc instead , we require that unc shall be a orthogonal matrix : unc Thus unc is our similar transformation of A into B. We then transform B into C : unc and so on , until the transform is eventually an upper triangular matrix having the eigenvalues of A in its diagonal . |
| 15 | We now repeat the cycle to obtain unc and so on . |