Operators and Keywords

Function List:


: norm (A)
: norm (A, p)
: norm (A, p, opt)

Compute the p-norm of the matrix A.

If the second argument is not given, p = 2 is used.

If A is a matrix (or sparse matrix):

p = 1

1-norm, the largest column sum of the absolute values of A.

p = 2

Largest singular value of A.

p = Inf or "inf"

Infinity norm, the largest row sum of the absolute values of A.

p = "fro"

Frobenius norm of A, sqrt (sum (diag (A' * A))).

other p, p > 1

maximum norm (A*x, p) such that norm (x, p) == 1

If A is a vector or a scalar:

p = Inf or "inf"

max (abs (A)).

p = -Inf

min (abs (A)).

p = "fro"

Frobenius norm of A, sqrt (sumsq (abs (A))).

p = 0

Hamming norm—the number of nonzero elements.

other p, p > 1

p-norm of A, (sum (abs (A) .^ p)) ^ (1/p).

other p p < 1

the p-pseudonorm defined as above.

If opt is the value "rows", treat each row as a vector and compute its norm. The result is returned as a column vector. Similarly, if opt is "columns" or "cols" then compute the norms of each column and return a row vector.

See also: normest, normest1, cond, svd.

Package: octave