math.linalg

dot and cross products, matrix multiply, determinant, inverse, linear systems

Example results generated on 2026-10-08. Ones using now, today or randomness will differ when you run them: press Run on any example to run it in your browser, after editing it if you like.

Functions

dot

dot(a: list, b: list): dot product of two vectors of the same length

dot([1, 2, 3], [4, 5, 6])
# → 32

See also: cross, norm

cross

cross(a: list, b: list): cross product of two 3-vectors

cross([1, 0, 0], [0, 1, 0])
# → [0, 0, 1]

See also: dot

norm

norm(v: list): length of a vector

norm([3, 4])
# → 5
norm([1 m, 1 m])
# → 1.41421 m

See also: dot, hypot

transpose

transpose(m: list): swap rows and columns

[[1, 2, 3], [4, 5, 6]].transpose
# → [[1, 4], [2, 5], [3, 6]]

See also: matmul

matmul

matmul(a: list, b: list): matrix product; a’s column count must match b’s row count

matmul([[1, 2], [3, 4]], [[5], [6]])
# → [[17], [39]]

See also: transpose, inv

det

det(m: list): determinant of a square matrix

det([[1, 2], [3, 4]])
# → -2

See also: inv, solve

inv

inv(m: list): inverse of a square matrix; exact for ints and fractions

inv([[4, 7], [2, 6]])
# → [[0.6, -0.7], [-0.2, 0.4]]

See also: det, solve

solve

solve(a: list, b: list): x such that a × x = b, for square a

solve([[2, 1], [1, 3]], [3, 5])
# → [0.8, 1.4]
solve([[1, 1, 1], [0, 2, 5], [2, 5, -1]], [6, -4, 27])
# → [5, 3, -2]

See also: inv, det

More examples

linalg

# solve 2x + y = 3, x + 3y = 5
solve([[2, 1], [1, 3]], [3, 5]).map(frac)
# → [4/5, 7/5]
# exact inverse
inv([[2, 1], [1, 1]])
# → [[1, -1], [-1, 2]]
# rotate (1, 0) by 90°
matmul([[cos(90 deg), -sin(90 deg)], [sin(90 deg), cos(90 deg)]], [[1], [0]])
# → [[6.12323e-17], [1]]
# distance between points
norm([3 m, 4 m])
# → 5 m