普通地质学6.2Properties of eigenvalues and eigenvectors普通地质学.pdf

Properties of eigenvalues and eigenvectors 1.What’s the relationship between the Outline matrix and its eigenvalues? 2.What’s the relationship between the matrix and its eigenvectors ? ◆Review Determine the eigenvalues and eigenvectors for the matrices below: −2 1 1  3 1 3 1    A 1 3, A 0 3, A  0 2 0 .     −4 1 3    1 2, 2 4, 1 2 3  =−1， k (1 0 1)T , k  0 1 1 1   k (−1,1) , k (1,1) ,    2 1 2 k (1,0) , (k  0) 2 3 (k1  0) (k2  0) k2 (1 4 0)T +k3 (0 −1 1)T k1, k2 are not both zeros  + 2 =+4  + 3 =+3  + + =−1+ 2+ 2 1 2 1 2 1 2 3 a11 +a22 3 =+3 a11 +a22 3 =+3 a11 +a22 =−2 +2 +3  8, det(A) 8  9, det(A) 9  =−4, det(A) =−4 1 2 1 2 1 2 ◼ Properties: The Product and Sum of the Eigenvalues Α (a ) has eigenvalues  ,  , ,  ，then ij nn 1 2 n (1)  + + + a =+a + +a ； 1