My Math Forum Projection onto eigenspace

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 April 18th, 2018, 09:13 PM #1 Newbie   Joined: Apr 2018 From: British Posts: 2 Thanks: 0 Projection onto eigenspace Hi, there is a question from my review sheet. A= 2 i -i 2 Let T = LA be a linear transformation, use the standard inner product space on C2. (a) Find the projections T1, T2 onto the eigenspaces of T. (b) Show T -1 as the combination of these projections. I am confused with what does the projection onto eigenspace mean. How can I find it? Use GramSch Process? Thanks
 April 20th, 2018, 10:33 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 You say you do not know what "projection onto eigenspace" means? Okay, do you know what and "eigenspace" is? Do you know what a "projection" is? The eigenspace of a Linear transformation is the subspace spanned by its eigenvectors. Have you found the eigenvalues of T? Have you found the eigenvectors corresponding to each of those eigenvalues? The projection of vector v onto a subspace S is the vector u in S such that v-u is orthogonal to S.

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