  ## Encyclopedia > Magnitude

Article Content

# Magnitude

In science, magnitude refers to the numerical size of something: see orders of magnitude.

In mathematics, the magnitude of an object is a non-negative real number, which in simple terms is its length.

In astronomy, magnitude refers to the logarithmic measure of the brightness of an object, measured in a specific wavelength or passband, usually in optical or near-infrared wavelengths: see apparent magnitude and absolute magnitude.

In geology, the magnitude is a logarithmic measure of the energy released during an earthquake. See Richter scale.

Real numbers The magnitude of a real number is usually called the absolute value or modulus. It is written | x |, and is defined by:

| x | = x , if x ≥ 0
| x | = -x , if x < 0

This gives the number's "distance from zero". For example, the modulus of -5 is 5.

Complex numbers Similarly, the magnitude of a complex number, called the modulus, gives the distance from zero in the Argand diagram. The formula for the modulus is the same as that for Pythagoras' theorem.

| x + iy | = √ ( x² + y² )

For instance, the modulus -3 + 4i is 5.

Euclidean vectors The magnitude of a vector of real numbers in a Euclidean n-space is most often the Euclidean norm, derived from Euclidean distance: the square root of the dot product of the vector with itself:

$s=\sqrt{u^2+v^2+w^2}$
where u, v and w are the components. For instance, the magnitude of [4, 5, 6] is √(42 + 52 + 62) = √77 or about 8.775.

General vector spaces A concept of length can be applied to a vector space in general. This is then called a normed vector space. The function that maps objects to their magnitudes is called a norm.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 Algeria ... in the northeast, Libya in the east, Niger in the southeast, Mali and Mauritania in the southwest, and Morocco in the west. Al Jumhūrīyah al ...  