diff --git a/src/RGBColorSpace.js b/src/RGBColorSpace.js
index ec3e35a0d..f31e56ff2 100644
--- a/src/RGBColorSpace.js
+++ b/src/RGBColorSpace.js
@@ -1,5 +1,5 @@
 import ColorSpace from "./ColorSpace.js";
-import {multiplyMatrices} from "./util.js";
+import {multiply_v3_m3x3} from "./util.js";
 import adapt from "./adapt.js";
 import XYZ_D65 from "./spaces/xyz-d65.js";
 
@@ -39,7 +39,7 @@ export default class RGBColorSpace extends ColorSpace {
 
 		if (options.toXYZ_M && options.fromXYZ_M) {
 			options.toBase ??= rgb => {
-				let xyz = /** @type {[number, number, number]} */ (multiplyMatrices(options.toXYZ_M, rgb));
+				let xyz = multiply_v3_m3x3(rgb, options.toXYZ_M);
 
 				if (this.white !== this.base.white) {
 					// Perform chromatic adaptation
@@ -51,7 +51,7 @@ export default class RGBColorSpace extends ColorSpace {
 
 			options.fromBase ??= xyz => {
 				xyz = adapt(this.base.white, this.white, xyz);
-				return multiplyMatrices(options.fromXYZ_M, xyz);
+				return multiply_v3_m3x3(xyz, options.fromXYZ_M);
 			};
 		}
 
diff --git a/src/adapt.js b/src/adapt.js
index 6bbe9e079..88f48bb5d 100644
--- a/src/adapt.js
+++ b/src/adapt.js
@@ -1,5 +1,5 @@
 import hooks from "./hooks.js";
-import {multiplyMatrices} from "./util.js";
+import {multiply_v3_m3x3} from "./util.js";
 
 // Type "imports"
 /** @typedef {import("./types.js").White} White */
@@ -70,7 +70,7 @@ export default function adapt (W1, W2, XYZ, options = {}) {
 	hooks.run("chromatic-adaptation-end", env);
 
 	if (env.M) {
-		return /** @type {[number, number, number]} */ (multiplyMatrices(/** @type {number[][]}*/ (env.M), env.XYZ));
+		return multiply_v3_m3x3(env.XYZ, env.M);
 	}
 	else {
 		throw new TypeError("Only Bradford CAT with white points D50 and D65 supported for now.");
diff --git a/src/multiply-matrices.js b/src/multiply-matrices.js
index aac838167..4af98d3dc 100644
--- a/src/multiply-matrices.js
+++ b/src/multiply-matrices.js
@@ -1,3 +1,8 @@
+// Type "imports"
+/** @typedef {import("./types.js").Matrix3x3} Matrix3x3 */
+/** @typedef {import("./types.js").Vector3} Vector3 */
+
+
 /**
  * A is m x n. B is n x p. product is m x p.
  *
@@ -85,3 +90,58 @@ export default function multiplyMatrices (A, B) {
 
 	return product;
 }
+
+
+// dot3 and transform functions adapted from https://github.com/texel-org/color/blob/9793c7d4d02b51f068e0f3fd37131129a4270396/src/core.js
+//
+// The MIT License (MIT)
+// Copyright (c) 2024 Matt DesLauriers
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+// IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+// DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
+// OR OTHER DEALINGS IN THE SOFTWARE.
+
+
+/**
+ * Returns the dot product of two vectors each with a length of 3.
+ *
+ * @param {Vector3} a
+ * @param {Vector3} b
+ * @returns {number}
+ */
+function dot3 (a, b) {
+	return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
+}
+
+/**
+ * Transforms a vector of length 3 by a 3x3 matrix. Specify the same input and output
+ * vector to transform in place.
+ *
+ * @param {Vector3} input
+ * @param {Matrix3x3} matrix
+ * @param {Vector3} [out]
+ * @returns {Vector3}
+*/
+export function multiply_v3_m3x3 (input, matrix, out = [0, 0, 0]) {
+	const x = dot3(input, matrix[0]);
+	const y = dot3(input, matrix[1]);
+	const z = dot3(input, matrix[2]);
+	out[0] = x;
+	out[1] = y;
+	out[2] = z;
+	return out;
+}
diff --git a/src/spaces/a98rgb-linear.js b/src/spaces/a98rgb-linear.js
index 4cf1bb57f..01153ab45 100644
--- a/src/spaces/a98rgb-linear.js
+++ b/src/spaces/a98rgb-linear.js
@@ -1,17 +1,25 @@
 import RGBColorSpace from "../RGBColorSpace.js";
 
+// Type "imports"
+/** @typedef {import("../types.js").Matrix3x3} Matrix3x3 */
+
 // convert an array of linear-light a98-rgb values to CIE XYZ
 // http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html
 // has greater numerical precision than section 4.3.5.3 of
 // https://www.adobe.com/digitalimag/pdfs/AdobeRGB1998.pdf
 // but the values below were calculated from first principles
 // from the chromaticity coordinates of R G B W
+
+
+/** @type {Matrix3x3} */
 const toXYZ_M = [
 	[ 0.5766690429101305,   0.1855582379065463,   0.1882286462349947  ],
 	[ 0.29734497525053605,  0.6273635662554661,   0.07529145849399788 ],
 	[ 0.02703136138641234,  0.07068885253582723,  0.9913375368376388  ],
 ];
 
+
+/** @type {Matrix3x3} */
 const fromXYZ_M = [
 	[  2.0415879038107465,    -0.5650069742788596,   -0.34473135077832956 ],
 	[ -0.9692436362808795,     1.8759675015077202,    0.04155505740717557 ],
diff --git a/src/spaces/acescg.js b/src/spaces/acescg.js
index 8b7d2ec4a..769fe52c1 100644
--- a/src/spaces/acescg.js
+++ b/src/spaces/acescg.js
@@ -2,6 +2,9 @@ import RGBColorSpace from "../RGBColorSpace.js";
 import {WHITES} from "../adapt.js";
 import "../CATs.js"; // because of the funky whitepoint
 
+// Type "imports"
+/** @typedef {import("../types.js").Matrix3x3} Matrix3x3 */
+
 // The ACES whitepoint
 // see TB-2018-001 Derivation of the ACES White Point CIE Chromaticity Coordinates
 // also https://github.com/ampas/aces-dev/blob/master/documents/python/TB-2018-001/aces_wp.py
@@ -9,11 +12,13 @@ import "../CATs.js"; // because of the funky whitepoint
 WHITES.ACES = [0.32168 / 0.33767, 1.00000, (1.00000 - 0.32168 - 0.33767) / 0.33767];
 
 // convert an array of linear-light ACEScc values to CIE XYZ
+/** @type {Matrix3x3} */
 const toXYZ_M = [
 	[  0.6624541811085053,   0.13400420645643313,  0.1561876870049078  ],
 	[  0.27222871678091454,  0.6740817658111484,   0.05368951740793705 ],
 	[ -0.005574649490394108, 0.004060733528982826, 1.0103391003129971  ],
 ];
+/** @type {Matrix3x3} */
 const fromXYZ_M = [
 	[  1.6410233796943257,   -0.32480329418479,    -0.23642469523761225  ],
 	[ -0.6636628587229829,    1.6153315916573379,   0.016756347685530137 ],
diff --git a/src/spaces/oklab.js b/src/spaces/oklab.js
index d915475e3..746446164 100644
--- a/src/spaces/oklab.js
+++ b/src/spaces/oklab.js
@@ -1,26 +1,35 @@
 import ColorSpace from "../ColorSpace.js";
-import {multiplyMatrices} from "../util.js";
+import {multiply_v3_m3x3} from "../util.js";
 import XYZ_D65 from "./xyz-d65.js";
 
+
+// Type "imports"
+/** @typedef {import("../types.js").Matrix3x3} Matrix3x3 */
+
+
 // Recalculated for consistent reference white
 // see https://github.com/w3c/csswg-drafts/issues/6642#issuecomment-943521484
+/** @type {Matrix3x3} */
 const XYZtoLMS_M = [
 	[ 0.8190224379967030, 0.3619062600528904, -0.1288737815209879 ],
 	[ 0.0329836539323885, 0.9292868615863434,  0.0361446663506424 ],
 	[ 0.0481771893596242, 0.2642395317527308,  0.6335478284694309 ],
 ];
 // inverse of XYZtoLMS_M
+/** @type {Matrix3x3} */
 const LMStoXYZ_M = [
 	[  1.2268798758459243, -0.5578149944602171,  0.2813910456659647 ],
 	[ -0.0405757452148008,  1.1122868032803170, -0.0717110580655164 ],
 	[ -0.0763729366746601, -0.4214933324022432,  1.5869240198367816 ],
 ];
+/** @type {Matrix3x3} */
 export const LMStoLab_M = [
 	[ 0.2104542683093140,  0.7936177747023054, -0.0040720430116193 ],
 	[ 1.9779985324311684, -2.4285922420485799,  0.4505937096174110 ],
 	[ 0.0259040424655478,  0.7827717124575296, -0.8086757549230774 ],
 ];
 // LMStoIab_M inverted
+/** @type {Matrix3x3} */
 export const LabtoLMS_M = [
 	[ 1.0000000000000000,  0.3963377773761749,  0.2158037573099136 ],
 	[ 1.0000000000000000, -0.1055613458156586, -0.0638541728258133 ],
@@ -48,22 +57,25 @@ export default new ColorSpace({
 	base: XYZ_D65,
 	fromBase (XYZ) {
 		// move to LMS cone domain
-		let LMS = multiplyMatrices(XYZtoLMS_M, XYZ);
+		let LMS = multiply_v3_m3x3(XYZ, XYZtoLMS_M);
 
 		// non-linearity
-		let LMSg = LMS.map(val => Math.cbrt(val));
-
-		return multiplyMatrices(LMStoLab_M, LMSg);
+		LMS[0] = Math.cbrt(LMS[0]);
+		LMS[1] = Math.cbrt(LMS[1]);
+		LMS[2] = Math.cbrt(LMS[2]);
 
+		return multiply_v3_m3x3(LMS, LMStoLab_M, LMS);
 	},
 	toBase (OKLab) {
 		// move to LMS cone domain
-		let LMSg = multiplyMatrices(LabtoLMS_M, OKLab);
+		let LMSg = multiply_v3_m3x3(OKLab, LabtoLMS_M);
 
 		// restore linearity
-		let LMS = LMSg.map(val => val ** 3);
+		LMSg[0] = LMSg[0] ** 3;
+		LMSg[1] = LMSg[1] ** 3;
+		LMSg[2] = LMSg[2] ** 3;
 
-		return multiplyMatrices(LMStoXYZ_M, LMS);
+		return multiply_v3_m3x3(LMSg, LMStoXYZ_M, LMSg);
 	},
 
 	formats: {
diff --git a/src/spaces/p3-linear.js b/src/spaces/p3-linear.js
index c14d38d46..cee96070e 100644
--- a/src/spaces/p3-linear.js
+++ b/src/spaces/p3-linear.js
@@ -1,11 +1,16 @@
 import RGBColorSpace from "../RGBColorSpace.js";
 
+// Type "imports"
+/** @typedef {import("../types.js").Matrix3x3} Matrix3x3 */
+
+/** @type {Matrix3x3} */
 const toXYZ_M = [
 	[0.4865709486482162, 0.26566769316909306, 0.1982172852343625],
 	[0.2289745640697488, 0.6917385218365064,  0.079286914093745],
 	[0.0000000000000000, 0.04511338185890264, 1.043944368900976],
 ];
 
+/** @type {Matrix3x3} */
 const fromXYZ_M = [
 	[ 2.493496911941425,   -0.9313836179191239, -0.40271078445071684],
 	[-0.8294889695615747,   1.7626640603183463,  0.023624685841943577],
diff --git a/src/spaces/prophoto-linear.js b/src/spaces/prophoto-linear.js
index e42f2aab6..3cff6707a 100644
--- a/src/spaces/prophoto-linear.js
+++ b/src/spaces/prophoto-linear.js
@@ -1,16 +1,21 @@
 import RGBColorSpace from "../RGBColorSpace.js";
 import XYZ_D50 from "./xyz-d50.js";
 
+// Type "imports"
+/** @typedef {import("../types.js").Matrix3x3} Matrix3x3 */
+
 // convert an array of  prophoto-rgb values to CIE XYZ
 // using  D50 (so no chromatic adaptation needed afterwards)
 // matrix cannot be expressed in rational form, but is calculated to 64 bit accuracy
 // see https://github.com/w3c/csswg-drafts/issues/7675
+/** @type {Matrix3x3} */
 const toXYZ_M = [
 	[ 0.79776664490064230,  0.13518129740053308,  0.03134773412839220 ],
 	[ 0.28807482881940130,  0.71183523424187300,  0.00008993693872564 ],
 	[ 0.00000000000000000,  0.00000000000000000,  0.82510460251046020 ],
 ];
 
+/** @type {Matrix3x3} */
 const fromXYZ_M = [
 	[  1.34578688164715830, -0.25557208737979464, -0.05110186497554526 ],
 	[ -0.54463070512490190,  1.50824774284514680,  0.02052744743642139 ],
diff --git a/src/spaces/rec2020-linear.js b/src/spaces/rec2020-linear.js
index 4d8935637..21a758b93 100644
--- a/src/spaces/rec2020-linear.js
+++ b/src/spaces/rec2020-linear.js
@@ -1,9 +1,13 @@
 import RGBColorSpace from "../RGBColorSpace.js";
 
+// Type "imports"
+/** @typedef {import("../types.js").Matrix3x3} Matrix3x3 */
+
 // convert an array of linear-light rec2020 values to CIE XYZ
 // using  D65 (no chromatic adaptation)
 // http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html
 // 0 is actually calculated as  4.994106574466076e-17
+/** @type {Matrix3x3} */
 const toXYZ_M = [
 	[ 0.6369580483012914, 0.14461690358620832,  0.1688809751641721  ],
 	[ 0.2627002120112671, 0.6779980715188708,   0.05930171646986196 ],
@@ -11,6 +15,7 @@ const toXYZ_M = [
 ];
 
 // from ITU-R BT.2124-0 Annex 2 p.3
+/** @type {Matrix3x3} */
 const fromXYZ_M = [
 	[  1.716651187971268,  -0.355670783776392, -0.253366281373660  ],
 	[ -0.666684351832489,   1.616481236634939,  0.0157685458139111 ],
diff --git a/src/spaces/srgb-linear.js b/src/spaces/srgb-linear.js
index 05528530d..0e3ff4e19 100644
--- a/src/spaces/srgb-linear.js
+++ b/src/spaces/srgb-linear.js
@@ -1,5 +1,8 @@
 import RGBColorSpace from "../RGBColorSpace.js";
 
+// Type "imports"
+/** @typedef {import("../types.js").Matrix3x3} Matrix3x3 */
+
 // This is the linear-light version of sRGB
 // as used for example in SVG filters
 // or in Canvas
@@ -7,6 +10,7 @@ import RGBColorSpace from "../RGBColorSpace.js";
 // This matrix was calculated directly from the RGB and white chromaticities
 // when rounded to 8 decimal places, it agrees completely with the official matrix
 // see https://github.com/w3c/csswg-drafts/issues/5922
+/** @type {Matrix3x3} */
 const toXYZ_M = [
 	[ 0.41239079926595934, 0.357584339383878,   0.1804807884018343  ],
 	[ 0.21263900587151027, 0.715168678767756,   0.07219231536073371 ],
@@ -15,6 +19,7 @@ const toXYZ_M = [
 
 // This matrix is the inverse of the above;
 // again it agrees with the official definition when rounded to 8 decimal places
+/** @type {Matrix3x3} */
 export const fromXYZ_M = [
 	[  3.2409699419045226,  -1.537383177570094,   -0.4986107602930034  ],
 	[ -0.9692436362808796,   1.8759675015077202,   0.04155505740717559 ],
diff --git a/src/types.d.ts b/src/types.d.ts
index f910708db..c757250e9 100644
--- a/src/types.d.ts
+++ b/src/types.d.ts
@@ -2,6 +2,11 @@
  * @packageDocumentation
  * Defines and re-exports many types for use throughout the library.
  */
+
+// muliply-matricies.js
+export type Matrix3x3 = [[number, number, number], [number, number, number], [number, number, number]];
+export type Vector3 = [number, number, number];
+
 // contrast/
 export type * from "./contrast/index.js";
 
@@ -104,8 +109,8 @@ export interface ParseFunctionReturn {
 
 // rgbspace.js
 export interface RGBOptions extends SpaceOptions {
-	toXYZ_M?: number[][] | undefined;
-	fromXYZ_M?: number[][] | undefined;
+	toXYZ_M?: Matrix3x3 | undefined;
+	fromXYZ_M?: Matrix3x3 | undefined;
 }
 
 // serialize.js
diff --git a/src/util.js b/src/util.js
index c7bb9c329..75d3403f4 100644
--- a/src/util.js
+++ b/src/util.js
@@ -2,7 +2,7 @@
  * Various utility functions
  */
 
-export {default as multiplyMatrices} from "./multiply-matrices.js";
+export {default as multiplyMatrices, multiply_v3_m3x3} from "./multiply-matrices.js";
 
 /**
  * Check if a value is a string (including a String object)
diff --git a/test/multiply_matrices.js b/test/multiply_matrices.js
index 89ec9332e..f02955368 100644
--- a/test/multiply_matrices.js
+++ b/test/multiply_matrices.js
@@ -1,5 +1,5 @@
 import * as math from "mathjs"; // Used as test oracle
-import multiplyMatrices from "../src/multiply-matrices.js";
+import {multiplyMatrices, multiply_v3_m3x3} from "../src/util.js";
 import * as check from "../node_modules/htest.dev/src/check.js";
 
 // Used to collect expected results from oracle
@@ -93,5 +93,25 @@ export default {
 				args: [[], []],
 			},
 		].map(expectThrows),
+	},
+	{
+		name: "Transform",
+		run: multiply_v3_m3x3,
+		tests: [
+			{
+				name: "3x3 matrix with vector",
+				args: [[1, .5, 0], M_lin_sRGB_to_XYZ],
+				expect: math.multiply(math.matrix(M_lin_sRGB_to_XYZ), math.matrix([1, .5, 0])).valueOf(),
+			},
+			{
+				name: "3x3 matrix with vector in place",
+				run (A, B) {
+					multiply_v3_m3x3(A, B, A);
+					return A;
+				},
+				args: [[1, .5, 0], M_lin_sRGB_to_XYZ],
+				expect: math.multiply(math.matrix(M_lin_sRGB_to_XYZ), math.matrix([1, .5, 0])).valueOf(),
+			},
+		],
 	}],
 };
diff --git a/types/test/RGBColorSpace.ts b/types/test/RGBColorSpace.ts
index 5867fa0c6..a620d83e9 100644
--- a/types/test/RGBColorSpace.ts
+++ b/types/test/RGBColorSpace.ts
@@ -13,6 +13,6 @@ new RGBColorSpace({
 new RGBColorSpace({
 	name: "RGBSpace",
 	id: "rgbspace",
-	toXYZ_M: [[1, 2, 3]],
-	fromXYZ_M: [[3, 2, 1]],
+	toXYZ_M: [[1, 2, 3], [4, 5, 6], [7, 8, 9]],
+	fromXYZ_M: [[3, 2, 1], [6, 5, 4], [9, 8, 7]],
 });