Difference between revisions of "Magnitude"
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A '''magnitude''' is a measure of the size of a mathematical entity. For example, the magnitude of a [[complex number]] is the distance from the number (graphed on the complex plane) to the origin, a measure of the size of a complex number. The magnitude is generally a positive real number. | A '''magnitude''' is a measure of the size of a mathematical entity. For example, the magnitude of a [[complex number]] is the distance from the number (graphed on the complex plane) to the origin, a measure of the size of a complex number. The magnitude is generally a positive real number. | ||
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| + | Formulaically, the magnitude of a real number <math>x</math> is its [[Absolute value | absolute value]] <math>|x|</math>, sometimes written <math>\sqrt{x^2}</math>. The magnitude <math>|z|</math> of a complex number <math>z</math> equals <math>\sqrt{Re(z)^2 + Im(z)^2}</math>. Both types of magnitude are bound by a form of the [[Triangle Inequality]] which states that <math>|a| + |b| \leq |a + b|</math>. | ||
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[[Category:Definition]] | [[Category:Definition]] | ||
Revision as of 21:32, 19 February 2022
A magnitude is a measure of the size of a mathematical entity. For example, the magnitude of a complex number is the distance from the number (graphed on the complex plane) to the origin, a measure of the size of a complex number. The magnitude is generally a positive real number.
Formulaically, the magnitude of a real number 
is its absolute value 
, sometimes written 
. The magnitude 
of a complex number 
equals 
. Both types of magnitude are bound by a form of the Triangle Inequality which states that 
.
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