Difference between revisions of "Magnitude"

Revision as of 18:52, 5 March 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 $x$ is its absolute value $|x|$ , sometimes written $\sqrt{x^2}$ . The magnitude $|z|$ of a complex number $z$ equals $\sqrt{\mathrm {Re}(z)^2 + \mathrm{Im}(z)^2}$ . Both types of magnitude are bound by a form of the Triangle Inequality which states that $|a| + |b| \geq |a + b|$ .

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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.
-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>.
+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{\mathrm {Re}(z)^2 + \mathrm{Im}(z)^2}</math>. Both types of magnitude are bound by a form of the [[Triangle Inequality]] which states that <math>|a| + |b| \geq |a + b|</math>.
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 [[Category:Definition]]

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Difference between revisions of "Magnitude"

Revision as of 18:52, 5 March 2022