GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
87 views

To find out the Eigen values we put the |A-⋋I | =0  why we put the determinant =0 .

Is there any specific reason For this

asked in Linear Algebra by Active (1k points)   | 87 views

1 Answer

+4 votes
Best answer

Yes, the concept is as follows:

Let A be a matrix and X, Y be 2 column vectors. Now a column vector X can be transformed into another column vector Y using a square matrix A as:

AX=Y

Now suppose Y is equal to a scalar multiple of X i.e. ⋋X . Then:

AX=Y=⋋X
AX-⋋IX=0
(A-⋋I)X=0


Hence   is known as an eigen value of matrix A and the corresponding non zero vector X as eigen vector.
 

 

answered by Active (1.3k points)  
selected by
Thanks I got the ans.
Top Users Feb 2017
  1. Arjun

    5224 Points

  2. Bikram

    4230 Points

  3. Habibkhan

    3748 Points

  4. Aboveallplayer

    2986 Points

  5. Debashish Deka

    2356 Points

  6. sriv_shubham

    2298 Points

  7. Smriti012

    2142 Points

  8. Arnabi

    2008 Points

  9. sh!va

    1654 Points

  10. mcjoshi

    1628 Points

Monthly Topper: Rs. 500 gift card

20,832 questions
25,989 answers
59,623 comments
22,046 users