I have two vectors v,w∈ in RR^n. Is the statement v^T w=w^T v true? In my opinion yes, because both are a single number, and this should be the same. Let v:= ((x),(y),(z)) and w:=((a),(b),(c))

evitagimm9h

evitagimm9h

Answered question

2022-11-08

I have two vectors v , w R n . Is the statement v T w = w T v true?
In my opinion yes, because both are a single number, and this should be the same.
Let v := ( x y z ) and w := ( a b c )
Then we get
v T w = ( x y z ) ( a b c ) = x a + y b + z c = a x + b y + c z = ( a b c ) ( x y z ) = w T v
because the multiplication is commutative.
Is this ok?

Answer & Explanation

siriceboynu1

siriceboynu1

Beginner2022-11-09Added 12 answers

Yes, it is correct . This is actually a way to define the (usual) dot product in R n : v w := v T w = w T v. (so remember this identity! It comes up a lot in linear algebra )

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