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zwingtip
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Homework Statement
Consider a linear transformation L from Rm to Rn. Show that there is an orthonormal basis {v1,...,vm} of Rm to Rn such that the vectors {L(v1),...,L(vm)} are orthogonal. Note that some of the vectors L(vi) may be zero. HINT: Consider an orthonormal basis {v1,...,vm} for the symmetric matrix ATA.
Homework Equations
if v1 and v2 are eigenvectors of a symmetric matrix with distinct eigenvalues [tex]\lambda_1[/tex] and [tex]\lambda_2[/tex], then v1 and v2 are orthogonal
The Attempt at a Solution
I have no idea how to even start this problem and I've been trying for a couple of days. Can anybody give me a tip as to how attack it? Thanks.