Complete the proof of Theorem 5.1.4: Orthogonal projection is linear transformation.
The transformation with respect to the basis is linear.
Consider the transformation defined as where, .
If the vector is perpendicular then .
Assume and , simplify as follows.
Further, simplify the equation as follows.
By the definition of linear transformation, the transformation is linear.
Hence, the transformation with respect to the basis is linear.
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