Inner product: Difference between revisions
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===Inner Product=== | ===Inner Product=== | ||
We will use the notation <math> <a|b> </math> to indicate the inner prodoct of <math>a</math> | We will use the notation <math> <a|b> </math> to indicate the inner prodoct of <math>a</math> with <math>b</math> is being taken. | ||
If we have two functions say <math>x(t)</math> and <math>y(t)</math>, then | If we have two functions, say <math>x(t)</math> and <math>y(t)</math>, then | ||
<math> <x(t)|y(t)> = \int_{a}^b x(t)^* y(t) dt </math> | <math> <x(t)|y(t)> = \int_{a}^b x(t)^* y(t) dt </math> | ||
Note: the <math> * </math> indicates that we are taking the [[complex conjugate]] of <math> x(t) </math>. We could just as easily have taken the complex conjugate of <math> y(t) </math>, but it is usually displayed as shown above. | Note: the <math> * </math> indicates that we are taking the [[complex conjugate]] of <math> x(t) </math>. We could just as easily have taken the complex conjugate of <math> y(t) </math>, but it is usually displayed as shown above, as a matter of tradition. | ||
Latest revision as of 16:54, 13 October 2005
Inner Product
We will use the notation to indicate the inner prodoct of with is being taken.
If we have two functions, say and , then
Note: the indicates that we are taking the complex conjugate of . We could just as easily have taken the complex conjugate of , but it is usually displayed as shown above, as a matter of tradition.