Theorem 7.1.1.Let A € M₂(C). Suppose A₁,...,Ak arethe distinct eigenvalues of A with multiplicities m₁,...,m², respectively. Then, there exists anon-singular matrix W such thatkW-AWT, where,Mm, (C), for 1 ≤iski=1and T's are upper triangular matrices with constant diagonal entry A. If A has real entrieswith real eigenvalues then W can be chosen to have real entries.DRAFT

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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e distinct eigenvalues of A with multiplicities m₁,...,mk, on-singular matrir W such the