Question

Prove that the eigen values of a SLBVP are real

Standard :- Msc 3rd semester ​

Answer 1

Answer:

The Spectral Theorem states that if A is an n × n symmetric matrix with real entries, then it has n orthogonal eigenvectors. The first step of the proof is to show that all the roots of the characteristic polynomial of A (i.e. the eigenvalues of A) are real numbers

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Answer 2

Step-by-step explanation:

Now, there is a guiding question as follows • Let λ and ϕ be an eigenvalue and a corresponding eigenfunction respectively. Let ϕ(x)=U(x)+iV(x) ...