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| | Emilia Shryock is my title but you can call me anything you like. Hiring is my profession. California is exactly where I've usually been residing and I adore every day residing right here. Doing ceramics is what her family members and her enjoy.<br><br>Here is my web-site ... [http://Nitv.in/dietfooddelivery78594 diet meal delivery] |
| {{Redirect|Conformable|the topic in [[geology]]|Unconformity}}
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| In [[mathematics]], a [[matrix (mathematics)|matrix]] is '''conformable''' if its dimensions are suitable for defining some operation (''e.g.'' addition, multiplication, etc.).
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| ==Examples==
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| * 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
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| ::<math>A + B = C</math>
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| :or
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| ::<math>A - B = C</math>
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| :for some fixed ''m'' and ''n''.
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| * For [[matrix multiplication]], consider the equation
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| ::<math>AB = C.</math>
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| :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.
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| * 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]].
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| *Only a square matrix is conformable for [[matrix inversion]]. However, the [[Moore-Penrose pseudoinverse]] and other [[generalized inverse]]s do not have this requirement.
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| * Only a square matrix is conformable for [[matrix exponentiation]].
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| ==See also==
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| * [[Linear algebra]]
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| {{DEFAULTSORT:Conformable Matrix}}
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| [[Category:Linear algebra]]
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| [[Category:Matrices]]
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Revision as of 14:57, 17 February 2014
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