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Unformatted text preview: roots in this case as 0 , , , 7 , 7 ,-5. When we use multiplicities and include complex roots, if any, then a polynomial of degree n has exactly n roots. It turns out that matrices A and B related by B = P-1 AP for some invertible matrix P share many important properties. Such matrices are said to be similar . Does it matter which side the inverse is on? FACT. Similar matrices have the same characteristic polynomial and so have the same eigenvalues with the same multiplicities. HOMEWORK: SECTION 5.2 EXAMPLE, IF TIME. Analyze the long-term behavior of the system dened by x k +1 = A x k when A = "-1 / 2 1 3 / 2 # and x = " 1 2 # ....
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- Spring '08