Matrix norms

Overview

The norm function computes the norm of a matrix or vector. The norm type is selected via the Norm enum.

Norm types

Enum value	Formula	Description
`Norm.Fro`	sqrt(sum of \\|a_ij\\|^2)	Frobenius norm (square root of sum of squares). Default.
`Norm.N1`	max over columns of sum \\|a_ij\\|	Maximum column sum (1-norm).
`Norm.Inf`	max over rows of sum \\|a_ij\\|	Maximum row sum (infinity norm).
`Norm.Max`	max(\\|a_ij\\|)	Maximum absolute element value.

Signatures

// Double matrix
fun LinAlg.norm(mat: MultiArray<Double, D2>, norm: Norm = Norm.Fro): Double

// Float matrix
fun LinAlg.norm(mat: MultiArray<Float, D2>, norm: Norm = Norm.Fro): Float

// Double vector
fun LinAlg.norm(mat: MultiArray<Double, D1>, norm: Norm = Norm.Fro): Double

// Float vector
fun LinAlg.norm(mat: MultiArray<Float, D1>, norm: Norm = Norm.Fro): Float

Parameters

Parameter	Type	Description
`mat`	`MultiArray<Double/Float, D2>` or `MultiArray<Double/Float, D1>`	Input matrix or vector.
`norm`	`Norm`	Norm type. Default: `Norm.Fro`.

Returns: Double or Float — the computed norm value.

Example

val a = mk.ndarray(mk[mk[1.0, 2.0], mk[3.0, 4.0]])

mk.linalg.norm(a)                // Frobenius: sqrt(1+4+9+16) = sqrt(30) ≈ 5.477
mk.linalg.norm(a, Norm.N1)       // max column sum: max(4, 6) = 6.0
mk.linalg.norm(a, Norm.Inf)      // max row sum: max(3, 7) = 7.0
mk.linalg.norm(a, Norm.Max)      // max |element|: 4.0

Vector norm

val v = mk.ndarray(mk[3.0, 4.0])

mk.linalg.norm(v)                // Frobenius: sqrt(9+16) = 5.0

19 February 2026