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c) Suppose that
,…,
, we have
,
,
.
d) Let u and v be vectors in an inner product space.
Prove that
if and only if
and
are orthogonal.
e) Let A be a square matrix such that
. What can you say about the eigenvalues of A?
f) Show that the matrix √
√ √
√ is orthogonal. Definition: A proper orthogonal matrix is an orthogonal matrix of which the determinant is equal to 1.
Check that P is not proper and deduce from P a proper orthogonal matrix P’. (Use a relevant small change only)...
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This note was uploaded on 02/07/2014 for the course MATH 218 taught by Professor Rananassif during the Summer '07 term at American University of Beirut.
 Summer '07
 RanaNassif
 Linear Algebra, Algebra

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