Norm

Norm(v)

returns the norm of the vector v

Norm(m, l)

computes the l-norm of matrix m (currently only works for vectors!).

Norm(m)

computes the norm of matrix m (SVD)

Norm(m, "Frobenius")

computes the Frobenius norm of matrix m

See

• Wikipedia - Norm (mathematics)
• Wikipedia - Matrix norm

Examples

>> Norm({1, 2, 3, 4}, 2)
Sqrt(30)

>> Norm({10, 100, 200}, 1)
310

>> Norm({a, b, c})
Sqrt(Abs(a)^2+Abs(b)^2+Abs(c)^2)

>> Norm({-100, 2, 3, 4}, Infinity)
100

>> Norm(1 + I)
Sqrt(2)

The first Norm argument should be a number, vector, or matrix.

>> Norm({1, {2, 3}})
Norm({1, {2, 3}})

>> Norm({x, y})
Sqrt(Abs(x)^2+Abs(y)^2)

>> Norm({x, y}, p)
(Abs(x) ^ p + Abs(y) ^ p) ^ (1 / p)

>> Norm({{1,2}, {3,4}})
5.46499

The second argument of Norm, 0, should be a symbol, Infinity, or an integer or real number not less than 1 for vector p-norms; or 1, 2, Infinity, or “Frobenius” for matrix norms.

>> Norm({x, y}, 0)
Norm({x, y}, 0)

The second argument of Norm, 0.5, should be a symbol, Infinity, or an integer or real number not less than 1 for vector p-norms; or 1, 2, Infinity, or “Frobenius” for matrix norms.

>> Norm({x, y}, 0.5)
Norm({x, y}, 0.5)

>> Norm({})
Norm({})

>> Norm(0)
0

Implementation status

• ✅ - full supported

Github

• Implementation of Norm