noun

eigenvalue

EYE-gun-val-yoo

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Eigenvalue (noun) means 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. Example: “The matrix has two real eigenvalues.”

noun

technical 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.

"The matrix has two real eigenvalues."

"To find the eigenvalues, you solve the characteristic equation of the matrix."

"Each eigenvalue of the transformation corresponds to a direction that is only stretched, not rotated."

How to use eigenvalue

Learner’s notes

In plain EnglishAn eigenvalue tells you by how much a matrix scales a special vector that keeps pointing the same way.

When to use it

It is a technical term used mainly in mathematics, physics and engineering.

Memory tip

An eigenvalue always comes paired with an eigenvector, so it helps to learn the two terms together.

Trace the full origin ↓

Easily confused with

eigenvector

Common pairings

calculate the eigenvalues real eigenvalue eigenvalue and eigenvector largest eigenvalue

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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”.

Test yourself on “eigenvalue” A quick quiz — meaning, synonyms & usage →

Fill the gap

Can you complete this real example?

The matrix has two real _____.

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.

Origin: German (via calque)

Synonyms

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characteristic value characteristic root proper value

Rhymes for eigenvalue

rue due sue cue hue blue true flue clue glue imbue pique

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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.

What is the meaning of eigenvalue?

"eigenvalue" (noun) means 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.