# Merge tags conditioning and condition-number?

I'd like to suggest merging these two tags for the following reasons.

• Both tags are under-utilized; many questions cover the topic of matrix conditioning, either in statement or in answers, but are not tagged as such. This may occur in part due to tag ambiguity.
• There are only 4 questions tagged with compared to 16 with , but the topics covered are essentially identical.
• The notions of matrix conditioning and condition number are inextricably linked; the former refers to the magnitude of the latter.

Is there any reason we should keep these tags separate or hesitate in enacting a global merge?

## 1 Answer

Conceptually, I think one should keep both tags. Mainly because they cannot be merged in a straight-forward manner.

1. The tag is commonly understood as referring to the special case of of linear systems. Thus, it seems necessary to keep the tag 'conditioning' as it contains both.
2. As indicated by the number of questions, the 'condition-number' is of particular interest and, thus, should be kept as a tag.

EDIT: However, in practice, because of rare appearance and because it can be replaced by a combination of 'condition-number' and 'nonlinear-equations' in case it indeed refers to nonlinear problems, I think it is safe to abandon the tag .

• In what sense is conditioning used not in reference to linear systems? At least 3 of the 4 posts tagged with conditioning refer to the conditioning of linear systems, and thus implicitly to condition number. – Ben May 28 '13 at 15:37
• Generally, conditioning is about error propagation of a functional. If $f$ measures the deviation in the solution $x$ of $Ax=b$ for a disturbance in $b$, one ends up with a parameter that is referred to as condition number. – Jan May 28 '13 at 16:51
• But I see your point. Obviously, 'conditioning' is not needed here. And it can be safely replaced by the combination 'condition-number' and 'nonlinear-equations', since the condition number is also defined for (the linearization of) nonlinear operations. Let me edit my answer accordingly. – Jan May 28 '13 at 16:58