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April 18th, 2018, 09:13 PM   #1
Joined: Apr 2018
From: British

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Question 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?

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April 20th, 2018, 10:33 AM   #2
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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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