Linear Algebra & Eigenvectors

linear_algebra

#1

In the article at 5.1 How to find Eigenvectors of a matrix? the following is mentioned.
(A-c)x = 0 …….(1)
Once you find the determinant of the matrix (A-c) and equate to 0, you will get an equation in ‘c’ of the order depending upon the given matrix A.
It will be helpful if the above line be elaborated . Thanks in anticipation


#2

For this equation (A-c)x = 0 has to be true. There are two cases :

x needs to be zero , it means x has to be zero vector which makes no sense.

Hence the other term (A-c) has to be singular matrix which determinant is zero by property.

Det(A-c) = 0

As A (Matrix) will be known to us . So when you solve determinant equation by equating it to zero , you will get one equation in c .

When you solve equation in c , you will get solutions as c1, c2 ,c3 …

Take c1 as solution , put in above equation to get x1 and similary for c2, c3 …

Please let me know what more confusion you have on this.

Regards
Arihant