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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 on the real number line. 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 x 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:
where u, v and w are the components (also the notation |x| is used). For instance, the magnitude of [4, 5, 6] is √(42 + 52 + 62) = √77 or about 8.775.
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.
A magnitude is never negative. When comparing magnitudes, it is often helpful to use a logarithmic scale. real-world examples include the loudness of a soundThis article is about compression waves. For other meanings, see sound (disambiguation Sound is a mechanical compression and rarefaction or a longitudinal displacement wave that propagates through a medium (solid, liquid or gas). The speed of this propaga ( decibelThe decibel is a "dimensionless unit" (like percent) that is a measure of ratios on a logarithmic scale. Usually, it is ten times the base-10 logarithm of the ratio. It's not an SI unit, although the International Committee for Weights and Measures (BIPM)) or the brightnessBrightness is an attribute of visual perception in which a source appears to emit a given amount of light. Brightness" was formerly used as a synonym for the photometric term luminance and (incorrectly) for the radiometric term radiance''. Brightness" sho of a starFor alternate meanings see star (disambiguation Hubble Space Telescope of the Sagittarius Star Cloud in the Milky Way Galaxy. A star is any massive gaseous celestial body in outer space. Stars appear as shining points in the nighttime sky that twinkle bec.
To put it another way, often it is not meaningful to simply add and subtract magnitudes.
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