eigenvalue
3 synonyms for eigenvalue, grouped by meaning and by how common each one is.
Noun — In linear algebra, a scalar that, when a linear transformation is applied to its matching non-zero vector, produces the same effect as simply multiplying that vector by the scalar.
Synonyms
Rare, literary or technical
Precise, but they will stand out — check the sense before using one.
characteristic value
characteristic root
proper value
How to use eigenvalue
The word patterns that sound natural to a native speaker.
calculate the eigenvalues
real eigenvalue
eigenvalue and eigenvector
largest eigenvalue
It is a technical term used mainly in mathematics, physics and engineering.
Etymology
Eigenvalue is built from the prefix eigen- joined to the ordinary word value. It is a partial calque of the German word Eigenwert, meaning the English word value was substituted for the German Wert while eigen was kept.
Full origin of eigenvalue →Frequently asked questions
What is an eigenvalue in simple terms?
It is a number that shows how much a linear transformation stretches or shrinks a particular vector, called the eigenvector, without changing its direction.
How do you find an eigenvalue?
You solve the equation Ax = λx for a matrix A, finding the scalar values of λ for which a non-zero vector x exists.
Is eigenvalue the same as characteristic value?
Yes, characteristic value and characteristic root are older synonyms for the same concept, though eigenvalue is now the standard term.
