By definition, a determinant is the sum of the products of items in different rows and columns.

To get λ (n- 1), we can only take the product of elements on the diagonal.

(λ-a11) (λ-a22) ... (λ-artificial neural network)

Therefore, the n- 1 term coefficient of the characteristic polynomial is -(a 1 1+a22+)...+ An).

The characteristic polynomial = (λ-λ 1) (λ-λ 2)...(λ-λ n), and the coefficient of n- 1 is -(λ 1+λ2+)...+λn).

So a11+A22+...+ANN = λ1+λ 2+...+λ n.

|λE-A|=

|λ-a 1 1 -a 12...-a 1n|

|-a2 1 λ-a22....-a2n|

|....................|

|-an 1 -an2....λ-ann|

=(λ-λ 1)(λ-λ2)...(λ-λn)

λ^n-(a 1 1+a22+...+ann)λ^(n- 1)+...+(- 1)|A|

=λ^n-(λ 1+λ2+...+λn)λ^(n- 1)+...+(- 1)λ 1λ2...λn

Compare the coefficients with the same power and draw the above conclusions! ! !