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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 (1.1k points) | 122 views

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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 (1.5k points)
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Thanks I got the ans.


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