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
Absolute magnitude corresponds to absolute bolometric magnitude 4.74. Placing a radiation source (e.g. star) at the standard distance of 10 parsecs, it follows that the zero point of the apparent bolometric magnitude scale corresponds to irradiance . Using the IAU 2015 scale, the nominal total solar irradiance ("solar constant") measured at 1 astronomical unit () corresponds to an apparent bolometric magnitude of the Sun of −26.832. Following Resolution B2, the relation between a star's absolute bolometric magnitude and its luminosity is no longer directly tied to the Sun's (variable) luminosity: where The new IAU absolute magnitude scale permanently disconnects the scale from