diff --git a/maths/determinant.ts b/maths/determinant.ts
new file mode 100644
index 00000000..456154aa
--- /dev/null
+++ b/maths/determinant.ts
@@ -0,0 +1,73 @@
+/**
+ * @description
+ * Computes the determinant of the given matrix using elimination.
+ * - Rounding errors may occur for some matrices.
+ * - Only handles 6 decimal places. Rounds thereafter.
+ * @Complexity_Analysis
+ * Time complexity: O(n^3)
+ * Space Complexity: O(n^2)
+ * @param {number[][]} m - A square matrix (2D array)
+ * @return {number} - The determinant
+ * @example det([[1,1],[1,1]]) = 0
+ */
+
+function interchange(m: number[][], from: number, to: number): number[][] {
+ ;[m[to], m[from]] = [m[from], m[to]]
+ return m
+}
+
+function addition(
+ m: number[][],
+ from: number,
+ to: number,
+ c: number
+): number[][] {
+ m[to] = m[to].map((e, i) => e + c * m[from][i])
+ return m
+}
+
+function diagProduct(m: number[][]): number {
+ let product = 1
+ for (let i = 0; i < m.length; i++) {
+ product *= m[i][i]
+ }
+ return product
+}
+
+export function det(m: number[][]): number {
+ if (m.some((r) => r.length != m.length)) {
+ throw new Error('only square matrices can have determinants')
+ }
+
+ const decPlaces = 6
+ const epsilon = 1e-6
+
+ // track the number of applied interchange operations
+ let appliedICs = 0
+ for (let i = 0; i < m[0].length; i++) {
+ // partial pivotting
+ let idealPivot = null
+ let maxValue = 0
+ for (let j = i; j < m.length; j++) {
+ if (Math.abs(m[j][i]) > maxValue) {
+ maxValue = Math.abs(m[j][i])
+ idealPivot = j
+ }
+ }
+ if (idealPivot === null) {
+ return 0
+ }
+ if (idealPivot != i) {
+ m = interchange(m, i, idealPivot)
+ appliedICs++
+ }
+ // eliminate entries under the pivot
+ for (let j = i + 1; j < m.length; j++) {
+ if (Math.abs(m[j][i]) > epsilon) {
+ m = addition(m, i, j, -m[j][i] / m[i][i])
+ }
+ }
+ }
+ const result = diagProduct(m) * (-1) ** appliedICs
+ return parseFloat(result.toFixed(decPlaces))
+}
diff --git a/maths/test/determinant.test.ts b/maths/test/determinant.test.ts
new file mode 100644
index 00000000..c55e8718
--- /dev/null
+++ b/maths/test/determinant.test.ts
@@ -0,0 +1,89 @@
+import { det } from '../determinant'
+
+describe('determinant', () => {
+ test.each([
+ [
+ [
+ [1, 2],
+ [3, 4, 5]
+ ]
+ ],
+ [
+ [
+ [1, 2, 3],
+ [4, 5, 6]
+ ]
+ ],
+ [
+ [
+ [1, 2],
+ [3, 4],
+ [5, 6]
+ ]
+ ]
+ ])('should throw an error for non square matrix %p', (matrix) => {
+ expect(() => det(matrix)).toThrow(
+ 'only square matrices can have determinants'
+ )
+ })
+
+ test.each([
+ [
+ [
+ [1, 2],
+ [3, 4]
+ ],
+ -2
+ ],
+ [
+ [
+ [1, 1],
+ [1, 1]
+ ],
+ 0
+ ],
+ [
+ [
+ [1, 2],
+ [0, 0]
+ ],
+ 0
+ ],
+ [
+ [
+ [8, 1, 5],
+ [9, 3, 7],
+ [1, 4, 4]
+ ],
+ 8
+ ],
+ [
+ [
+ [15, 85, 32],
+ [76, 83, 23],
+ [28, 56, 92]
+ ],
+ -382536
+ ],
+ [
+ [
+ [2, -1, 0, 3],
+ [4, 0, 1, 2],
+ [3, 2, -1, 1],
+ [1, 3, 2, -2]
+ ],
+ -42
+ ],
+ [
+ [
+ [0.75483643, 0.68517541, 0.53548329, 0.5931435],
+ [0.37031247, 0.80103707, 0.82563949, 0.91266224],
+ [0.39293451, 0.27228353, 0.54093836, 0.51963319],
+ [0.60997323, 0.40161682, 0.58330774, 0.17392144]
+ ],
+ -0.051073
+ ]
+ ])('determinant of %p should be %d', (matrix, expected) => {
+ expect(det(matrix)).toBe(expected)
+ })
+})
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