Use the method of Examples 7 and 8 to find the Jordan normal form J of each
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Use the method of Examples 7 and 8 to find the Jordan normal form J of each coefficient matrix A given in Problems 23 through 32 (respectively).
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Example 7 In Example 3 we saw that the matrix ^=[03] A 7 = has the single eigenvalue > {V₁, V2), where V₁ = [-3 If we define 4 and the associated length 2 chain of generalized eigenvectors 3] and v₂ = [1 0], based on the eigenvector v₁ = Av₂. [3] Q=[V₁ V2] = then we find that the Jordan normal form of A is 4 J=Q-¹AQ = [1 4]. Here J = J₁ is a single 2 × 2 Jordan block corresponding to the single eigenvalue λ = 4 of A.
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V 803 1 0 V3 3 2 1 0 0 Q V V V3 V4 V J QAQ 13 2000 0 0 0 0 0 0 0 2 0 30...View the full answer
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Related Book For
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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