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Show that for every c suppose that we have d let

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Unformatted text preview: very 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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