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Eigenvector of 2x2 matrix

  • Thread starter Ry122
  • Start date
565
2
for the matrix
{5,0}
{2,-2}

when determining the eigenvector for its 2nd eigenvalue, -2, you would start out by doing


{5--2 ,0}
{2 ,-2--2}

giving

{7,0}
{2,0}

In equation form this is

7u + 0v = 0
2u + 0v = 0

Ordinarily I would set u or v to a value and solve for the other letter.


But in this case this can't be done since in both equations v has a coefficient of 0.


So what would you do in this situation?
 

phyzguy

Science Advisor
4,119
1,130
Clearly u=0, and the equations will both be satisfied for any value of v, so the normalized eigenvector is (0,1).
 

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