Difference between revisions of "Homogeneous"
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| − | A function <math>f(a_1,a_2,\ldots,a_n)</math> is said to be ''' | + | A function <math>f(a_1,a_2,\ldots,a_n)</math> is said to be '''homogeneous''' if all its terms are of the same degree in <math>a_i</math>. |
| − | This concept is often used in [[inequalities]] so that one can "scale" the terms, and assume things like the sum of the involved variables is <math>1</math>. | + | This concept is often used in [[inequalities]] so that one can "scale" the terms (this is possible because <math>f(ta_1,ta_2,\ldots,ta_n)=t^kf(a_1,a_2,\ldots,a_n)</math> for some fixed <math>k</math>), and assume things like the sum of the involved variables is <math>1</math>. |
{{stub}} | {{stub}} | ||
Revision as of 01:56, 13 February 2009
A function 
is said to be homogeneous if all its terms are of the same degree in 
.
This concept is often used in inequalities so that one can "scale" the terms (this is possible because 
for some fixed 
), and assume things like the sum of the involved variables is 
.
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