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.
|Table of contents|
2 Complex numbers
3 Euclidean vectors
4 General vector spaces
The magnitude of a real number is usually called the absolute value or modulus. It is written | x |, and is defined by:
This gives the number's "distance from zero". For example, the modulus of -5 is 5.
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.
For instance, the modulus of -3 + 4i is 5.
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:
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.