.. highlightlang:: us

.. index:: norm

.. _norm:

norm
====

.. us.tag  norm ENGLISH math-lin-alg

:ref:`norm` calculates various matrix norms.

.. function::  rsNorm = norm(m)
               rsNorm = norm(m, ssType)

.. us.return

**Return Value**

*rsNorm* is the matrix norm.

.. us.params

**Parameters**

.. uparam:: m

   is a real or complex matrix.

.. uparam:: ssType

   is an option string that sets the matrix norm. It can have one
   of the following values:

   .. list-table::
      :header-rows: 1

      * - Value
        - Meaning
      * - ``"1"``
        - 1-Norm (maximum column sum).
      * - ``"2"``
        - 2-Norm (maximum singular value).
      * - ``"I"`` oder "Inf"
        - Infinit Norm (maximum row sum).
      * - ``"F"`` oder "Frob"
        - Frobenius-Norm (Square root of the sum of the aquare of the matrix elements).
      * - ``"M"`` oder "Max"
        - Maximum-Norm (maximum of the absolute value).

.. us.comment

**Comment**

*ssType* is not case sensitive.

.. us.example

**Example**

::

   * a = [1,2,3;4,5,6;7,8,9]
   * a
      1.0000    2.0000    3.0000
      4.0000    5.0000    6.0000
      7.0000    8.0000    9.0000
   * // Calculate various
   * // Matrix Norms:
   * norm(a)
      18.0000
   * norm(a, "1")     // 1-Norm
      18.0000
   * max(sum(abs(a)))
      18.0000
   * norm(a, "2")    // 2-Norm
      16.8481
   * norm(a, "Inf")    // Infinit-Norm
      24.0000
   * max(sum(abs(a')))
      24.0000
   * norm(a, "Frob")    // Frobenius-Norm
      16.8819
   * sqrt(sum(sum(a.*a)))
      16.8819
   * norm(a, "m")         // Maximum-Norm
       9.0000
   * max(max(abs(a)))
       9.0000

.. seealso::
   :ref:`cond`

:sub:`id-796612`