noun

eigenvector

EYE-gun-vek-tor

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Eigenvector (noun) means In linear algebra, a vector that keeps its direction and is only stretched or shrunk, not rotated, when a particular linear transformation is applied to it. Example: “Engineers find the eigenvectors of a stiffness matrix to work out a structure's natural modes of vibration.”

noun

technical In linear algebra, a vector that keeps its direction and is only stretched or shrunk, not rotated, when a particular linear transformation is applied to it.

"Engineers find the eigenvectors of a stiffness matrix to work out a structure's natural modes of vibration."

"In data analysis, the eigenvectors of a covariance matrix point along the directions where the data varies most."

"Every eigenvector has a matching eigenvalue that tells you how much it is scaled."

How to use eigenvector

Learner’s notes

In plain EnglishAn eigenvector is a direction that a transformation stretches or shrinks but does not turn.

When to use it

It is a specialist mathematical term used mainly in linear algebra, physics and engineering.

Memory tip

Keep eigenvector and eigenvalue apart: the vector is a direction, the value is the scaling factor that goes with it.

Trace the full origin ↓

Easily confused with

eigenvalue →

Common pairings

eigenvector of a matrix corresponding eigenvector dominant eigenvector eigenvalue and eigenvector

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C2 · Advanced serendipity Fortunate discoveries made entirely by accident.

Gen Z slang rizz Charm — the ability to attract a romantic interest.

B2 · Intermediate empathy The capacity to share another person’s feelings.

C1 · Advanced nonchalant Casually calm and relaxed; unconcerned.

Internet slang delulu Delusional — believing something against the odds.

Etymology nostalgia Greek nostos “return home” + algos “pain”.

C2 · Advanced serendipity Fortunate discoveries made entirely by accident.

Gen Z slang rizz Charm — the ability to attract a romantic interest.

B2 · Intermediate empathy The capacity to share another person’s feelings.

C1 · Advanced nonchalant Casually calm and relaxed; unconcerned.

Internet slang delulu Delusional — believing something against the odds.

Etymology nostalgia Greek nostos “return home” + algos “pain”.

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Fill the gap

Can you complete this real example?

Engineers find the _____ of a stiffness matrix to work out a structure's natural modes of vibration.

Etymology

Formed from the prefix eigen- attached to vector, closely following the German word Eigenvektor. The mathematician David Hilbert first used the eigen- prefix in 1904, and he may have taken the idea from an earlier related use by Hermann von Helmholtz.

Origin: English

Synonyms

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characteristic vector latent vector proper vector

Rhymes for eigenvector

vector hector rector sector ejector Spector bisector director detector defector injector inspector

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Frequently asked questions

What is an eigenvector in simple terms?

It is a vector that, under a given linear transformation, only gets longer, shorter or flipped, rather than turned to point in a new direction.

What is the difference between an eigenvector and an eigenvalue?

The eigenvector is the direction that stays fixed under the transformation, while the eigenvalue is the number that says how much the eigenvector is scaled.

Where does the word eigenvector come from?

It combines the German-derived prefix eigen- with the English word vector, closely mirroring the German term Eigenvektor.

What is the meaning of eigenvector?

"eigenvector" (noun) means in linear algebra, a vector that keeps its direction and is only stretched or shrunk, not rotated, when a particular linear transformation is applied to it.