The following representation: (a+beta′ X)^2 where a is a constant and both beta and X are k by 1 vectors.

Hagman7v 2022-09-14 Answered
I have the following representation:
( a + β X ) 2
where a is a constant and both β and X are k by 1 vectors.
The representation is further written as follows:
a 2 + 2 a β X + X β β X )
While the first part is clear to me, I struggle to understand why it is shown once with ′ (X′ and β ) and once without ′ (X and β).
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Answers (1)

cercimw
Answered 2022-09-15 Author has 8 answers
here denotes the transpose vector. Since both β and X are k × 1 vectors, β X is a scalar, so β X = ( β X ) = X β, and
( β X ) 2 = ( β X ) ( β X ) = X β β X .

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