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Unformatted text preview: r 1 and r 2 with corresponding eigenvectors (1) = 11 21 and (2) = 12 22 . Denote the 2 2 matrices D = r 1 r 2 and T = 11 12 21 22 . The Frst matrix is constructed from the eigenvalues, whereas the second is constructed from the eigenvectors. We will show that T 1 AT = D . To this end, recall the formula for the inverse of a matrix: 11 12 21 22 1 = 1 11 22 12 21 22 12 21 11 . Then we have the matrix product T 1 AT = 1 11 22 12 21 22 12 21 11 a 11 a 12 a 21 a 22 11 12 21 22 = 1 11 22 12 21 22 12 21 11 r 1 11 r 2 12 r 1 21 r 2 22 = r 1 r 2 = D . 1...
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue UniversityWest Lafayette.
 Spring '09
 EdrayGoins
 Matrices

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