Question

7.3. Examine the eigenvalues of the family of matrices 「-2 1 0 0 1 0 0 一2 1 Dr =-N- 10 where Dv is N x N, for growing values of N, for example, N 32,64,128. The smallest eigenvalues converge to integer multiples of a simple number. 7.4. Verify, for a random 10 x 5 matrix, the identity i=1 where K-minrn, n), {σ1, . . . ,CK} are the singular values of A, and 11-11 F is the Frobenius matrix norm.

I need 7.3. This is a matlab question and I don't know what simple number is.

Answer 1

Your Code 1 A-rand(10,5); 2 e-svd (A); 3 e_s-sum(e. 2) An-norm(A,' fro' )"2
OUTPUT:

Result... executed in 1.821 sec(s) es-17.626 A n-17.626
COPY CODE:

A=rand(10,5);
e=svd(A);
e_s=sum(e.^2)
A_n=norm(A,'fro')^2