Eigenvalues and eigenvectors

Overview

Multik provides two functions for eigenvalue computation:

Function	Description
`eig`	Computes both eigenvalues and eigenvectors.
`eigVals`	Computes eigenvalues only (more efficient when vectors are not needed).

Both functions return complex results because eigenvalues of a real matrix can be complex.

eig

Computes the eigenvalues and eigenvectors of a square matrix.

Signatures

fun <T : Number> LinAlg.eig(mat: MultiArray<T, D2>): Pair<D1Array<ComplexDouble>, D2Array<ComplexDouble>>
fun LinAlg.eig(mat: MultiArray<Float, D2>): Pair<D1Array<ComplexFloat>, D2Array<ComplexFloat>>
fun <T : Complex> LinAlg.eig(mat: MultiArray<T, D2>): Pair<D1Array<T>, D2Array<T>>

Parameters

Parameter	Type	Description
`mat`	`MultiArray<T, D2>`	Square matrix to decompose.

Returns: Pair<eigenvalues, eigenvectors> where:

eigenvalues — a 1D array of complex eigenvalues.
eigenvectors — a 2D matrix whose columns are the corresponding eigenvectors.

Example

val a = mk.ndarray(mk[mk[4.0, -2.0], mk[1.0, 1.0]])

val (values, vectors) = mk.linalg.eig(a)
// values: [3.0+0.0i, 2.0+0.0i]
// vectors: columns are eigenvectors for each eigenvalue

eigVals

Computes only the eigenvalues of a square matrix (without eigenvectors).

Signatures

fun <T : Number> LinAlg.eigVals(mat: MultiArray<T, D2>): D1Array<ComplexDouble>
fun LinAlg.eigVals(mat: MultiArray<Float, D2>): D1Array<ComplexFloat>
fun <T : Complex> LinAlg.eigVals(mat: MultiArray<T, D2>): D1Array<T>

Parameters

Parameter	Type	Description
`mat`	`MultiArray<T, D2>`	Square matrix.

Returns: D1Array of complex eigenvalues.

Example

val a = mk.ndarray(mk[mk[2.0, 1.0], mk[1.0, 2.0]])

val eigenvalues = mk.linalg.eigVals(a)
// [3.0+0.0i, 1.0+0.0i]

Pitfalls

Eigenvalue results are always complex (ComplexDouble or ComplexFloat), even for symmetric matrices where all eigenvalues are real. Access the real part with .re and imaginary part with .im.
The input matrix must be square. Non-square matrices will cause an error.
The pure Kotlin engine does not support eig or eigVals — use the OpenBLAS or default engine.

19 February 2026