Linear Algebra: How to represent this transformation as a matrix?

  • Thread starter zeion
  • Start date
  • #1
467
0

Homework Statement



Find the spectrum of the given linear operator T on V and find an eigenvector of T corresponding to each eigenvalue.

[tex]

V = R_{2x2}, T (\begin{bmatrix}a_{11}&a_{12}\\a_{21}&a_{22} \end{bmatrix}) = \begin{bmatrix}-2a_{11}-a_{12}&a_{11}\\a_{21}&2a_{22} \end{bmatrix}

[/tex]

Homework Equations





The Attempt at a Solution



I'm confused about how to write the columns and rows of the transformation matrix.. do I do this:

[tex]


\begin{bmatrix}-2&-1&0&0\\1&0&0&0\\0&0&1&0\\0&0&0&2 \end{bmatrix}


[/tex]

Or the transposed? Or something else?

When I tried to get the spectrum (eigenvalues?) of this matrix I get {1, 2, -2} but the answer is {1,-1,2}, which doesn't work with the characteristic polynomial..
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
That's one way to write the matrix. Though to be absolutely clear you should say which columns correspond to which basis vector. But I get eigenvalues {1,-1,2} for your matrix. Maybe just check your eigenvalue calculation.
 

Related Threads on Linear Algebra: How to represent this transformation as a matrix?

Replies
6
Views
1K
Replies
8
Views
1K
Replies
2
Views
571
Replies
13
Views
161
  • Last Post
Replies
18
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
1
Views
1K
Replies
5
Views
27K
Replies
6
Views
728
Top