Conformable matrix: Difference between revisions

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Revision as of 05:38, 21 March 2006

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A [[matrix (mathematics)|matrix]] in [[mathematics]] is '''conformable''' if its dimensions are suitable for defining some operation (''e.g.'' addition, multiplication, etc.). In order to be conformable to addition, matrices need to have the same dimension, so that in

In order to be conformable to addition, matrices need to have the same dimension. Thus ''A'', ''B'' and ''C'' all must have dimension ''m'' × ''n'' in the equation

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

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

A, B and C all have to have the same <math>m \times n</math> dimension. For multiplication, in the formula

For [[matrix multiplication]], consider the equation

<math> A*B = C</math>,

:<math> A*BAB = C.</math>,

if A has dimension <math>m \times n</math>, then B has to be <math>n \times p</math> for some p, giving C as <math>m \times p.</math>

ifIf ''A'' has dimension <math>''m'' \&times; ''n</math>'', then ''B'' has to behave <math>dimension ''n'' \&times; ''p</math>'' for some ''p'', giving ''C'' as <math>''m'' \&times; ''p''.</math>

==See also==