The reason behind the name "Orthogonal transformation". An orthogonal transformation is a linear transformation such that $(Tx,Ty)=(x,y)$. 
Orthogonality is suggestive of perpendicularity. What might have been the reason for naming a distance preserving linear transformation on a vector space "orthogonal"?
Thanks!

I have insufficient reputation to add a comment, so I'll expand Carsten's comment into a response.
Like you say, an orthogonal transformation satisfies $(Tx, Ty) = (x,y)$.  Let's look at some simple consequences.  First off, if $x\perp y$, so that $(x,y) = 0$,
then $Tx\perp Ty$.  This is one reason $T$ might be called orthogonal: it preserves orthogonality of vectors.
Another thing we can do is look at the dual map $:T^*:V\to V$, which satisfies 
$(Tx, y) = (x, T^*y)$.  (Here I've identified $V$ with its dual, since we have defined an inner product on $V$).  If $V$ is a finite-dimensional space over $\mathbb{R}$, and $(x, y) = y^T x$, and $T$ is represented by multiplication by a matrix, then $T^*$ is multiplication by its transpose.  To see this, we just
compute
$$
(Tx, y) = y^T Tx = (y^T Tx)^T = x^T T^T y = (x, T^*y).
$$
Now if we use the orthogonality condition, we have $(Tx, Ty) = (x, T^*Ty) = (x,y)$.  Thus, $T^*T = Id$ is the identity operation.  In terms of matrices,
this means that the rows of $T$ must be orthogonal to each other.  Similarly,
since $TT^* = Id$, the columns of $T$ must also be orthogonal.  This is another sense in which $T$ is orthogonal.
