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
Richter magnitude scale used by astronomers. Second, he wanted a magnitude of zero to be around the limit of human perceptibility. Third, he specified the Wood-Anderson seismograph as the standard instrument for producing seismograms. Magnitude was then defined as "the logarithm of the maximum trace amplitude, expressed in microns", measured at a distance of 100 km. The scale was calibrated by defining a magnitude 3 shock as one that produces (at a distance of 100 km) a maximum amplitude of 1 micron (1 µm, or 0.001 millimeters) on a seismogram recorded by a Wood-Anderson torsion seismograph. Finally, Richter calculated a table of distance