Sage-Tips

Is Eigen German?

Borrowed from German eigen (“own”). Many of the compounds represent partial translations from German, e.g. eigenvalue from German Eigenwert. Doublet of own.

What does Eigen mean in eigenvalue?

As far as I understand it, the ‘eigen’ in words like eigenvalue, eigenvector etc. means something like ‘own’, or a better translation in English would perhaps be ‘characteristic’. Each square matrix has some special scalars and vectors associated with it.

Why is Eigen called Eigen?

Eigen is a German term that means “own” which is a good way to think of values or vectors that are “characteristic” of a matrix. They used to be called “proper values” but early mathemeticians including Hilbert and the Physician Helmholtz coined the term eigenvalues and eigenvectors.

How do you use Eigen in German?

“eigen” is one of the adjectives that can go with a dative that denotes ownership in elevated (and, somewhat archaic) language. Your example is formed that way: Die Macht über die Bürger ist dem Staate eigen. Die Frau sei dem Manne untertan.

Where do eigenvalues come from?

Exactly; see Eigenvalues : The prefix eigen- is adopted from the German word eigen for “proper”, “inherent”; “own”, “individual”, “special”; “specific”, “peculiar”, or “characteristic”.

What is Eigen line?

So, an eigenvector of A is a nonzero vector v such that Av and v lie on the same line through the origin. In this case, Av is a scalar multiple of v ; the eigenvalue is the scaling factor.

What does Eigen mean in physics?

The word “eigenstate” is derived from the German/Dutch word “eigen”, meaning “inherent” or “characteristic”. An eigenstate is the measured state of some object possessing quantifiable characteristics such as position, momentum, etc.

Where does the word Eigen come from?

The prefix eigen- is adopted from the German word eigen for “proper”, “inherent”; “own”, “individual”, “special”; “specific”, “peculiar”, or “characteristic”.

How are eigenvalues used in real life?

Oil companies frequently use eigenvalue analysis to explore land for oil. Oil, dirt, and other substances all give rise to linear systems which have different eigenvalues, so eigenvalue analysis can give a good indication of where oil reserves are located.

https://www.youtube.com/watch?v=kwA3qM0rm7c