Solved: Let B be an n × n symmetric matrix such that B2 =

Chapter 7, Problem 36E

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

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