Let T : R n R n be a linear transformation that preserves lengths; that is,

Question:

Let T : Rn Rn be a linear transformation that preserves lengths; that is, ΙΙT(x)ΙΙ = ΙxΙΙ  for all x in Rn.

a. Show that T also preserves orthogonality; that is, T(x) · T(y) = 0 whenever x · y = 0.

b. Show that the standard matrix of T is an orthogonal matrix.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

Question Posted: