Linear algebra

Overview

The mk.linalg entry point provides linear algebra operations on 2D matrices and 1D vectors. Functions are defined in the LinAlg and LinAlgEx interfaces; convenience extension functions and infix operators are also available.

Most functions accept Number, Float, and Complex types through separate overloads. Numeric overloads typically return Double results; float overloads preserve Float precision.

Operations

Operation	Function	Description
Dot product	`dot`	Matrix-matrix, matrix-vector, or vector-vector product.
Matrix inverse	`inv`	Inverse of a square matrix.
Matrix power	`pow`	Raise a square matrix to an integer power.
QR decomposition	`qr`	Decompose into orthogonal Q and upper-triangular R.
PLU decomposition	`plu`	Decompose into permutation P, lower-triangular L, upper-triangular U.
SVD	`svd`	Singular value decomposition (experimental).
Eigenvalues	`eig`	Eigenvalues and eigenvectors.
Eigenvalues only	`eigVals`	Eigenvalues without eigenvectors.
Solve	`solve`	Solve a linear system Ax = b.
Norms	`norm`	Matrix or vector norm (Frobenius, 1-norm, infinity, max).

Type support

Each operation has up to three overloads:

Overload	Input type	Output type
Default	`MultiArray<T: Number, D2>`	`Double`/`NDArray<Double, …>`
Float (`…F`)	`MultiArray<Float, D2>`	`Float`/`NDArray<Float, …>`
Complex (`…C`)	`MultiArray<T: Complex, D2>`	`NDArray<T, …>`

Quick example

val a = mk.ndarray(mk[mk[1.0, 2.0], mk[3.0, 4.0]])
val b = mk.ndarray(mk[mk[5.0, 6.0], mk[7.0, 8.0]])

// Dot product
val c = mk.linalg.dot(a, b)        // 2×2 matrix product

// Inverse
val aInv = mk.linalg.inv(a)        // inverse of a

// Solve Ax = b
val x = mk.linalg.solve(a, mk.ndarray(mk[1.0, 2.0]))

19 February 2026