Difference between revisions of "ℓ1 Norm Distance Function"

From GM-RKB
Jump to: navigation, search
m (Text replacement - "“" to "“")
m (Remove links to pages that are actually redirects to this page.)
 
Line 1: Line 1:
 
An [[ℓ1 Norm Distance Function|ℓ1 norm distance function]] is a [[Minkowski distance function]] with <math>d=1</math> (that represents the [[shortest]] [[distance]] in [[unit step]]s along each [[axis]] between two [[point]]s).
 
An [[ℓ1 Norm Distance Function|ℓ1 norm distance function]] is a [[Minkowski distance function]] with <math>d=1</math> (that represents the [[shortest]] [[distance]] in [[unit step]]s along each [[axis]] between two [[point]]s).
* <B>AKA:</B> [[Taxicab Geometry]], [[Manhattan/Rectilinear Distance]], <math>\ell_1</math>.
+
* <B>AKA:</B> [[ℓ1 Norm Distance Function|Taxicab Geometry]], [[Manhattan/Rectilinear Distance]], <math>\ell_1</math>.
 
* <B>Context</U>:</B>
 
* <B>Context</U>:</B>
 
** It can be defined as  <math>\|\mathbf{x}\|_1 := \sum_{i=1}^{n} |x_i|.</math>
 
** It can be defined as  <math>\|\mathbf{x}\|_1 := \sum_{i=1}^{n} |x_i|.</math>

Latest revision as of 20:45, 23 December 2019

An ℓ1 norm distance function is a Minkowski distance function with [math]d=1[/math] (that represents the shortest distance in unit steps along each axis between two points).



References

2015

2011



2010

2009

  • (Weisstein, 2009-11-02) ⇒ Eric W. Weisstein. (2009). “L1-Norm." From MathWorld - A Wolfram Web Resource. http://mathworld.wolfram.com/L1-Norm.html
    • A vector norm defined for a vector [math]\mathbf{x}=[x_1, x_2, ..., x_n][/math], with complex entries by [math]|x|_1=\sum_{r=1}^n|x_r|[/math]. The [math]L^1[/math]-norm [math]|x|_1[/math] of a vector [math]x[/math] is ...

2008

1990

  • (Horn & Johnson, 1990) ⇒ R. A. Horn, and C. R. Johnson. (1990). “Norms for Vectors and Matrices." Ch. 5 in Matrix Analysis. Cambridge University Press.