If A is a 3 xx 3-matrix, while x and y are a vector point with x,y,z. Why is the dot product of ⟨A ** x,y⟩ the same as the dot product of ⟨A′ ** y,x⟩. (A′ being the transposed matrix)

lollaupligey9 2022-08-13 Answered
If A is a 3 × 3-matrix, while x and y are a vector point with x,y,z. Why is the dot product of A x , y the same as the dot product of A y , x
(A′ being the transposed matrix)
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Answers (1)

Brooks Hogan
Answered 2022-08-14 Author has 18 answers
For column vectors u , v , the scalar product is
u , v = u T v .
Therefore
A x , y = ( A x ) T y = x T A T y = x , A T y = A T y , x .
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