Complex random vector

In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a> and <a href="/facts/Statistics/DNPsKGYU">statistics</a>, a complex random vector is typically a <a href="/facts/Tuple/BI1HIxL8">tuple</a> of <a href="/facts/Complex_number/2w7mqI7e">complex</a>-valued <a href="/facts/Random_variable/TwTBXnLT">random variables</a>, and generally is a random variable taking values in a <a href="/facts/Vector_space/M1pxMLx2">vector space</a> over the <a href="/facts/Field_(mathematics)/xAjAS4ko">field</a> of complex numbers. If 
 
 
 
 
 Z
 
 1
 
 
 ,
 …
 ,
 
 Z
 
 n
 
 
 
 
 {\displaystyle Z_{1},\ldots ,Z_{n}}
 
 are complex-valued random variables, then the n-tuple 
 
 
 
 
 (
 
 
 Z
 
 1
 
 
 ,
 …
 ,
 
 Z
 
 n
 
 
 
 )
 
 
 
 {\displaystyle \left(Z_{1},\ldots ,Z_{n}\right)}
 
 is a complex random vector. Complex random variables can always be considered as pairs of real random vectors: their real and imaginary parts.
Some concepts of real random vectors have a straightforward generalization to complex random vectors. For example, the definition of the mean of a complex random vector. Other concepts are unique to complex random vectors.
Applications of complex random vectors are found in <a href="/facts/Digital_signal_processing/PEG7azr8">digital signal processing</a>.

Complex random vector open-in-new

Complex random vector