The Relationship Between Sets of Reciprocal Vectors
Theorem
If
and
are sets of reciprocal vectors, and
(1) then
Proof
Since
andare perpendicular sets,
Substitute (1) into these expressions, obtaining
Then
Now use the identity
hence
Theorem
Ifandare sets of reciprocal vectors, and(1) then
Proof
Sinceandare perpendicular sets,
Substitute (1) into these expressions, obtaining
Then
Now use the identityhence