3.1.P15 Let n ≥ 2, let x, y e C" be given nonzero vectors, and let A = xy*. (a) Showthat the Jordan canonical form of A is B On-2, in which B =[*]if y*x #0 andB == J2(0) if y*x = 0. (b) Explain why a rank-one matrix is diagonalizable if and only ifits trace is nonzero.

Given: n≥2, x,y∈ℂn are non zero vectors. A=xy* B=y*x000 Show that: (a) Jordan…

3.1.P15 Let n ≥ 2, let x, y € C" be given nonzero vectors, and let A = xy*. (a) Show if y*x #0 and 0 0 that the Jordan canonical form of A is B On-2, in which B = B = J₂(0) if y*x = 0. (b) Explain why a rank-one matrix is diagonalizable if and only if its trace is nonzero.

3.1.P15 Let n ≥ 2, let x, y € C" be given nonzero vectors, and let A = xy. (a) Show if yx #0 and 0 0 that the Jordan canonical form of A is B On-2, in which B = B = J₂(0) if y*x = 0. (b) Explain why a rank-one matrix is diagonalizable if and only if its trace is nonzero.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Determinants

Section3.CM: Cumulative Review

Problem 29CM

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Question

3.1.P15 Let n ≥ 2, let x, y e C" be given nonzero vectors, and let A = xy*. (a) Show
that the Jordan canonical form of A is B On-2, in which B =
[*]if y*x #0 and
B =
= J2(0) if y*x = 0. (b) Explain why a rank-one matrix is diagonalizable if and only if
its trace is nonzero.

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