2
votes
1answer
47 views

Question about compact operator

So here is my question, Let $H$ be a Hilbert-space and $K:H\rightarrow H$ a compact operator. I know that if $K$ is self adjoint, then it has one eigenvalue $\mu$ such that $|\mu|=||K||$. Can some ...
0
votes
1answer
27 views

Hermitian matrices and their eigenvalues

Let $C=A+B$ where $A$ and $B$ are two hermitian matrices can I prove that $\lambda_{i,C}=\lambda_{i,A}+\lambda_{i,B}$ iff $x_{i,A}=x_{i,B}$? Where $x_i$ is the eigenvector related to eigenvalue ...
1
vote
2answers
280 views

Example of eigenvectors in different bases (follow-up question)

This is a follow-up question on this one: Connection between eigenvalues and eigenvectors of a matrix in different bases Assume I have matrix $$ B=\left( \begin{array}{cccc} 0 & 0 & 1 ...
6
votes
3answers
3k views

Examples for proof of geometric vs. algebraic multiplicity

Here you see a supposedly easy proof of a well-known theorem in linear algebra: Although I know I should understand this, I don't :-( Obviously there are too many indices and stuff, so I don't see ...
9
votes
6answers
4k views

How are eigenvectors/eigenvalues and differential equations connected?

In school and at university we never had eigenvalues nor differential equations, so these concepts were really giving me a hard time. Now I developed some intuition for both concepts. I learned that ...