Magnitude

Magnitude in mathematics refers to a non-negative real number that describes how large an object is or the distance between two objects.

Magnitude of a complex number

The magnitude of a real number or of any other complex number is its absolute value, denoted |x| for the absolute value of x. For instance, the magnitude of -3.51 is 3.51, and the magnitude of -3 + 4i is 5.

Magnitude of a vector

The magnitude of a vector of real numbers in a Euclidean n-space is most often the Euclidean norm, the square root of the dot product of the vector with itself. For instance, the magnitude of [4, 5, 6] is 4² + 5² + 6² = √(77) or about 8.775.

Magnitude in general

Only objects in a normed vector space have a magnitude. The function that maps objects to their magnitudes is called a norm.

See also:

• Apparent magnitude
• Absolute magnitude
• Order of magnitude

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