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EXAMPLE 6 Standard Matrix for a Projection Operator
Let l be the line in the -plane that passes through the origin and makes an angle with the positive x-axis, where . As
illustrated in Figure 4.3.5a, let be a linear operator that maps each vector into its orthogonal projection on l.
Figure 4.3.5
(a) Find the standard matrix for T. onto the line through the origin that makes an angle of with
(b) Find the orthogonal projection of the vector
the positive x-axis.
Solution (a)
