Eigen

The German word eigen is used as a prefix in technical and scientific English to denote the characteristic or proper value of a variable, often a vector. The term eigenvalue began to replace the English term “proper value” in this context at the start of the twentieth century, offering a more distinctive and memorable word which is now typically used with linear algebra and matrix theory in mathematics and physics.  The technical terms eigenvalue, eigenquation, eigenvector, eigenspaces, eigenbasis and eigendecomposition are all currently in use in English.

The German adjective eigen corresponds to the English adjective own, in the sense of one’s own, or what is proper or characteristic. Adding the suffix -schaft to create an abstract noun actually gives the German word Eigenschaft, meaning a characteristic. Adding the suffix -tum to describe a condition or collective idea yields the German noun Eigentum, meaning property or possession.