Exercise 3.3.7. Given the two vectors and find the projection matrix that projects onto the subspace spanned by and .
Answer: The subspace spanned by and is the column space where
The projection matrix onto the subspace is then . We have
Since is a diagonal matrix we can compute its inverse by simply taking the reciprocals of the diagonal entries:
We then have
NOTE: This continues a series of posts containing worked-out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books.