# column operations

## column operations

[′käl·əm ‚äp·ə′rā·shənz]
(mathematics)
A set of rules for manipulating the columns of a matrix so that the image of the corresponding linear transformation remains unchanged.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
This new white paper from Mettler Toledo's experts explores how ISM's Plug and Measure and predictive diagnostics features, as well as its automated sensor maintenance, can significantly improve ion exchange column operations.
Performing the indicated column operations (where [C.sub.i] [right arrow] [C.sub.i] [right arrow] [C.sub.1] indicates the column operation of subtracting the 1st column from the ith column, 2 [less than or equal to] i [less than or equal to] n), we get
We perform the indicated column operations (where [C.sub.1] [right arrow] [C.sub.1] + C2 + ::: + Cn indicates the operation of adding all the columns and then replacing the 1st column by that sum, and [C.sub.1] [right arrow] 1 / [C.sub.1] + C2 + ...
To prove the result for n+1, we consider the determinant of order n+1, and perform the indicated column operations (where [C.sub.1] [right arrow] [C.sub.1] + [C.sub.n] indicates the operation of adding the n - th column to the 1st column to get the new 1st column), to get
In this case, starting with the determinant [B.sub.n] = [B.sub.2m], we perform the indicated column operations.
We perform the indicated row and column operations to reduce the determinant
One can perform several column operations, including autofill row-based formulas.
Such analysis can be performed by packed column or capillary column operations using appropriate apparatus, both procedures having particular advantages, but when the proportion of "non normal" or iso alkane hydrocarbon is high, the latter technique, using "cold on column" injection finds favor, due to inherently greater resolving power.
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