Find the Largest Eigenvalue & Eigenvector of A

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Homework Help Overview

The discussion revolves around finding the largest eigenvalue and corresponding eigenvector of a matrix A defined as A = a.a', where a is an N by 1 vector and a'a = 5. Participants are exploring the properties of eigenvalues and eigenvectors in the context of matrix algebra.

Discussion Character

  • Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Some participants suggest generating an example vector to construct the matrix A and analyze the results. Others express confusion regarding the definition of A, questioning the nature of the expression a.a' and its implications for matrix dimensions.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the definitions and properties of the matrix involved. There is an indication of confusion about the mathematical setup, and some guidance has been offered regarding the construction of A.

Contextual Notes

There is a mention of a misunderstanding regarding the dimensions of the matrix A, as well as the scalar nature of a'a. This suggests that assumptions about the problem setup may need further examination.

akanksha331
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A=a.a', where a is an N by 1 vector,a'a=5,and T is transpose.
a)Give the largest eigenvalue of A.
b)what is the corresponding eigenvector?

Please help me to solve the problem.
 
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To get started see if you can generate an example vector and construct A and see what the answer is for that case. Then ask what choices you had in your example and whether any of those choices change the problem.
 
I'm rather confused, because ## a \cdot a'## is a number not a matrix. Where are you supposed to get A from?
 
aa' is a NxN matrix. It's a'a that is a scalar.akanksha331, read your personal messages. This thread is closed.
 

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