In mathematics, the magnitude of an object is a nonnegative 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 nearinfrared 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:
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.
For instance, the modulus 3 + 4i is 5.
Euclidean vectors The magnitude of a vector of real numbers in a Euclidean nspace 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.
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