Let uj,..., u, be an orthogonal basis for a subspace W of R", and let T : R" → R" be defined by T(x) = projw X. Show that T is a linear transformation.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 1CM
Question
Let uj,..., u, be an orthogonal basis for a subspace W of R", and let T : R" → R" be defined by
T(x) = projw X. Show that T is a linear transformation.
Transcribed Image Text:Let uj,..., u, be an orthogonal basis for a subspace W of R", and let T : R" → R" be defined by T(x) = projw X. Show that T is a linear transformation.
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