1) Let A EM^*^ (IR) by a real nxn matnx, and suppose it has an eigenvalue λ with eigenvector v. (part) Suppose A has a generalized eigenvector w, such that (A-AI)ŵ = v by direct computation, venfy that at Y₁ = ev 7₁e (0) are both solutions to ₁ = Ay 1 (part ii) Under the assumption of parti), suppose A has another generalized eigenvector" ū, such that By direct computation, venfy that (A-1) u = w 1 1₁ = e at (ü + + t + 2 v) Is another Solution to = Ai Generalized eigenvector of A in general means (A-21)^ i=0 for some k ≥2

1) Let A EM^*^ (IR) by a real nxn matnx, and suppose it has an eigenvalue λ with eigenvector v. (part) Suppose A has a generalized eigenvector w, such that (A-AI)ŵ = v by direct computation, venfy that at Y₁ = ev 7₁e (0) are both solutions to ₁ = Ay 1 (part ii) Under the assumption of parti), suppose A has another generalized eigenvector" ū, such that By direct computation, venfy that (A-1) u = w 1 1₁ = e at (ü + + t + 2 v) Is another Solution to = Ai Generalized eigenvector of A in general means (A-21)^ i=0 for some k ≥2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 8BEXP

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