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Unformatted text preview: x 1 and x 2 are the columns of S , what are the eigenvalues and eigenvectors of B = S ± 2 1 ² S1 , C = S ± 2 3 1 ² S1 ? 4 MATH 108 B FALL 2011 EXTRACREDIT PROBLEMS –3) (a) Show that if B is unitary and λ ∈ C is an eigenvalue of B , then  λ  = 1. (b) Show that if A is normal (i.e. A * A = AA * ) and invertible, then B = A * A1 is unitary. MATH 108 B FALL 2011 EXTRACREDIT PROBLEMS 5 –4) Show that A = ± 1 ² . has no square root, i.e. there is no B such that B 2 = A ....
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 Fall '07
 RickRugangYe
 Linear Algebra, Eigenvectors, Vectors, Matrices, Orthogonal matrix, Normal matrix, EXTRACREDIT PROBLEMS

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