Let B be an n x n symmetric matrix such that B 2 = B. Any such
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Let B be an n x n symmetric matrix such that B2 = B. Any such matrix is called a projection matrix (or an orthogonal projection matrix). Given any y in Rn, let ŷ = By and z = y = ŷ.
a. Show that z is orthogonal to ŷ.
b. Let W be the column space of B. Show that y is the sum of a vector in W and a vector in W⊥?. Why does this prove that By is the orthogonal projection of y onto the column space of B?
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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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