Magnitude (mathematics) their magnitudes is called a norm. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. Not all vector spaces are normed. In a pseudo-Euclidean space, the magnitude of a vector is the value of the quadratic form for that vector. When comparing magnitudes, a logarithmic scale is often used. Examples include the loudness of a sound (measured in decibels), the brightness of a star, and the Richter scale of earthquake intensity. Logarithmic magnitudes can be negative. It is not meaningful to simply add or subtract them. Orders of magnitude denote differences
Magnitude (astronomy) by astronomers are: The difference between these concepts can be seen by comparing two stars. Betelgeuse (apparent magnitude 0.5, absolute magnitude −5.8) appears slightly dimmer in the sky than Alpha Centauri (apparent magnitude 0.0, absolute magnitude 4.4) even though it emits thousands of times more light, because Betelgeuse is much farther away. Under the modern logarithmic magnitude scale, two objects, one of which is used as a reference or baseline, whose intensities (brightnesses) measured from Earth in units of power per unit area (such as watts per square metre, W m) are and , will have magnitudes and related by