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Problem 3. a) A Jordan block Jm(A) is an m xm matrix of the form. 0 1 0 1 00X 000 Suppose A e End (C"). Prove that the number dim ker((A-A1)) - dim ker((A - A1)-¹) is equal to the number of Jordan blocks in the Jordan normal form of A of size greater than or equal to r. b) Find the Jordan normal form for Jm (A)².

Problem 3. a) A Jordan block Jm(A) is an m xm matrix of the form. 0 1 0 1 00X 000 Suppose A e End (C"). Prove that the number dim ker((A-A1)) - dim ker((A - A1)-¹) is equal to the number of Jordan blocks in the Jordan normal form of A of size greater than or equal to r. b) Find the Jordan normal form for Jm (A)².

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 3. a) A Jordan block Jm(A) is an m x m matrix of the form. 0 0 1 0 0 1 44 0 00 Suppose A E End (C"). Prove that the number 0 dim ker((A-A1)) - dim ker((A-X1))) is equal to the number of Jordan blocks in the Jordan normal form of A of size greater than or equal to r. b) Find the Jordan normal form for Jm (A)².
Transcribed Image Text:Problem 3. a) A Jordan block Jm(A) is an m x m matrix of the form. 0 0 1 0 0 1 44 0 00 Suppose A E End (C"). Prove that the number 0 dim ker((A-A1)) - dim ker((A-X1))) is equal to the number of Jordan blocks in the Jordan normal form of A of size greater than or equal to r. b) Find the Jordan normal form for Jm (A)².
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