Let A, BE MInn(R) be two square matrices. i) Explain what it means that the matrices A and B are similar, i.e., A~ B. ii) Prove that if the matrices A and B are similar, then the the characteristic polyno- mial of the matrix A equals to the characteristic polynomial of the matrix B, i.e., PA(:) = Pa(:). iii) Give an example of two matrices A, BE M2.2(C) such that A) A is not similar to B; and B) PA(:) = PA(:). Give a detailed justification to your answer. %3D

Let A, BE MInn(R) be two square matrices. i) Explain what it means that the matrices A and B are similar, i.e., A~ B. ii) Prove that if the matrices A and B are similar, then the the characteristic polyno- mial of the matrix A equals to the characteristic polynomial of the matrix B, i.e., PA(:) = Pa(:). iii) Give an example of two matrices A, BE M2.2(C) such that A) A is not similar to B; and B) PA(:) = PA(:). Give a detailed justification to your answer. %3D

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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