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.
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a To show that T preserves orthogonality we need to demonstrate that for any vectors x and y in Rn i...View the full answer
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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