3. Let A be an orthonormal transform, and let y = Ax. Let the squared norm of a vector be defined as ||x|| ² = x²x = Σx?². Show that ||y|| = |x||². That is, orthonormal transform preserves the norm (or energy of the signal).
3. Let A be an orthonormal transform, and let y = Ax. Let the squared norm of a vector be defined as ||x|| ² = x²x = Σx?². Show that ||y|| = |x||². That is, orthonormal transform preserves the norm (or energy of the signal).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Let A be an orthonormal transform, and let y
=
Ax. Let the squared norm of a vector be
defined as ||x|| ² = x²x = Σx². Show that ||y|| = ||x||². That is, orthonormal transform preserves the
norm (or energy of the signal).
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