Who introduced the concept of eigenvalues and eigenvectors and where does the name come from? Is there a connection with the German word "eigen"?
Exactly; see Eigenvalues :
The prefix eigen- is adopted from the German word eigen for "proper", "inherent"; "own", "individual", "special"; "specific", "peculiar", or "characteristic".
It was David Hilbert who introduced the terms Eigenwert and Eigenfunktion; see:
- David Hilbert, Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen (1904); see e.g. page X for Eigenwert and Eigenfunktion [see here for the English translation].