Friction stir welding

2014-01-29T18:52:17Z

162.93.65.2: Removed a paragraph of blatant product placement: "The DeltaN FS® system is a tool for friction stir welding developed by EADS Innovation Works"

{{Unreferenced|date=December 2009}}
{{Redirect|Conformable|the topic in [[geology]]|Unconformity}}

In [[mathematics]], a [[matrix (mathematics)|matrix]] is '''conformable''' if its dimensions are suitable for defining some operation (''e.g.'' addition, multiplication, etc.).

==Examples==
* In order to be conformable to addition or subtraction, matrices need to have the same dimensions. Thus ''A'', ''B'' and ''C'' all must have dimensions ''m'' × ''n'' in the equation

::<math>A + B = C</math>

:or

::<math>A - B = C</math>

:for some fixed ''m'' and ''n''.

* For [[matrix multiplication]], consider the equation

::<math>AB = C.</math>

:If ''A'' has dimensions ''m'' × ''n'', then ''B'' has to have dimensions ''n'' × ''p'' for some ''p'', so that ''C'' will have dimensions ''m'' × ''p''. That is, the number of columns in ''A'' must equal the number of rows in ''B'' for ''A'' and ''B'' to be conformable for multiplication in that sequence.

* Since squaring a matrix involves multiplying it by itself (<math>A^2=AA</math>) a matrix must be ''m''×''m'' (that is, it must be a [[square matrix]]) to be conformable for squaring. Thus for example only a square matrix can be [[Idempotent matrix|idempotent]].

*Only a square matrix is conformable for [[matrix inversion]]. However, the [[Moore-Penrose pseudoinverse]] and other [[generalized inverse]]s do not have this requirement.

* Only a square matrix is conformable for [[matrix exponentiation]].

==See also==
* [[Linear algebra]]

{{DEFAULTSORT:Conformable Matrix}}
[[Category:Linear algebra]]
[[Category:Matrices]]

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Friction stir welding