norm

..  norm(A, [p])

Compute the ``p``-norm of a vector or the operator norm of a matrix ``A``, defaulting to the ``p=2``-norm.

For vectors, ``p`` can assume any numeric value (even though not all values produce a mathematically valid vector norm). In particular, ``norm(A, Inf)`` returns the largest value in ``abs(A)``, whereas ``norm(A, -Inf)`` returns the smallest.

For matrices, the matrix norm induced by the vector ``p``-norm is used, where valid values of ``p`` are ``1``, ``2``, or ``Inf``. (Note that for sparse matrices, ``p=2`` is currently not implemented.) Use :func:`vecnorm` to compute the Frobenius norm.

Examples

The norm function in Julia calculates the p-norm of a vector or the operator norm of a matrix A. By default, it computes the p=2-norm.

norm(A, [p])

For vectors, the parameter p can take any numeric value, although not all values produce a mathematically valid vector norm. The norm(A, Inf) returns the largest value in abs(A), while norm(A, -Inf) returns the smallest.

For matrices, the p-norm used is the matrix norm induced by the vector p-norm. Valid values for p are 1, 2, or Inf. Note that for sparse matrices, p=2 is currently not implemented. To compute the Frobenius norm, use the vecnorm function.

Here are some examples of using the norm function:

Compute the Euclidean norm of a vector:
```
julia> v = [3, 4];
julia> norm(v)
5.0
```

Compute the p=1 norm of a vector:

julia> w = [-1, 2, -3];
julia> norm(w, 1)
6.0

Compute the p=Inf norm of a matrix:

julia> A = [1 2; -3 4];
julia> norm(A, Inf)
7.0

Compute the Frobenius norm of a matrix using vecnorm:

julia> B = [1 2; 3 4; 5 6];
julia> vecnorm(B)
9.539392014169456

Please note that these examples assume that the necessary variables are defined before using the norm function.

Ac_ldiv_B, Ac_ldiv_Bc, Ac_mul_B, Ac_mul_Bc, Ac_rdiv_B, Ac_rdiv_Bc, At_ldiv_B, At_ldiv_Bt, At_mul_B, At_mul_Bt, At_rdiv_B, At_rdiv_Bt, A_ldiv_Bc, A_ldiv_Bt, A_mul_B!, A_mul_Bc, A_mul_Bt, A_rdiv_Bc, A_rdiv_Bt, Bidiagonal, cond, conv2, det, diag, diagind, diagm, diff, eig, eigvals, eigvecs, expm, eye, full, inv, isdiag, ishermitian, isposdef, isposdef!, issym, istril, istriu, logabsdet, logdet, lyap, norm, qrfact, rank, repmat, rot180, rotl90, rotr90, sortrows, sqrtm, SymTridiagonal, trace, Tridiagonal, tril, tril!, triu, triu!, writedlm,

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norm

Examples

See Also

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