diff --git a/src/number/arithmetic.js b/src/number/arithmetic.js
index 71d3d6e..dd03106 100644
--- a/src/number/arithmetic.js
+++ b/src/number/arithmetic.js
@@ -49,5 +49,10 @@ export const sqrt = match(NumberT, (math, _N, strategy) => {
    })
 })
 
-export const subtract = plain((a, b) => a - b)
+export const subtract = [
+   plain((a, b) => a - b),
+   match([Undefined, NumberT], Returns(NumberT, () => NaN)),
+   match([NumberT, Undefined], Returns(NumberT, () => NaN))
+]
+
 export const quotient = plain((a,b) => Math.floor(a/b))
diff --git a/src/vector/__test__/arithmetic.spec.js b/src/vector/__test__/arithmetic.spec.js
index 4ca9c54..77337b3 100644
--- a/src/vector/__test__/arithmetic.spec.js
+++ b/src/vector/__test__/arithmetic.spec.js
@@ -24,6 +24,12 @@ describe('Vector arithmetic functions', () => {
       assert.deepStrictEqual(
          add([[1, 2], [4, 2]], [0, -1]), [[1, 1], [4, 1]])
    })
+   it('negates a vector', () => {
+      assert.deepStrictEqual(math.negate([-3, 4, -5]), [3, -4, 5])
+   })
+   it('subtracts vectors', () => {
+      assert.deepStrictEqual(math.subtract([-3, 4, -5], [8, 0, 2]), [-11, 4, -7])
+   })
    it('computes the sum of a vector', () => {
       const sum = math.sum
       assert.strictEqual(sum([-3, 4, -5]), -4)
diff --git a/src/vector/arithmetic.js b/src/vector/arithmetic.js
index 1ca31bb..4803148 100644
--- a/src/vector/arithmetic.js
+++ b/src/vector/arithmetic.js
@@ -16,6 +16,9 @@ export const normsq = match(Vector, (math, V) => {
 export const abs = promoteUnary('abs')
 export const add = promoteBinary('add')
 
+export const negate = promoteUnary('negate')
+export const subtract = promoteBinary('subtract')
+
 export const sum = match(Vector, (math, V) => {
    const add = math.add.resolve([V.Component, V.Component])
    const haszero = math.haszero(V.Component)