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Norm

Matrix norms induced by vector p-norms (SymPy, WMA)

Norm[m, p]

computes the p-norm of matrix m.

Norm[m]

computes the 2-norm of matrix m.

The Norm of of a vector is its Euclidean distance:

• • Norm[{x, y, z}]

By default, 2-norm is used for vectors, but you can be explicit:

• • Norm[{3, 4}, 2]

The 1-norm is the sum of the values:

• • Norm[{10, 100, 200}, 1]

• • Norm[{x, y, z}, Infinity]

• • Norm[{-100, 2, 3, 4}, Infinity]

For complex numbers, Norm[z] is Abs[z]:

• • Norm[1 + I]

So the norm is always real, even when the input is complex.

Norm[m,“Frobenius”] gives the Frobenius norm of m:

• • Norm[Array[Subscript[a, ##] &, {2, 2}], "Frobenius"]