Editing Distance matrix (section)

== Additive distance matrix ==
An additive distance matrix is a special type of matrix used in [[bioinformatics]] to build a [[phylogenetic tree]]. Let {{mvar|x}} be the lowest common ancestor between two species {{mvar|i}} and {{mvar|j}}, we expect {{mvar|1=''M{{sub|ij}}'' = ''M{{sub|ix}}'' + ''M{{sub|xj}}''}}. This is where the additive metric comes from. A distance matrix {{mvar|M}} for a set of species {{mvar|S}} is said to be additive if and only if there exists a phylogeny {{mvar|T}} for {{mvar|S}} such that:

* Every edge {{math|(''u'',''v'')}} in {{mvar|T}} is associated with a positive weight {{mvar|d{{sub|uv}}}}
* For every {{math|''i'',''j'' ∈ ''S''}}, {{mvar|M{{sub|ij}}}} equals the sum of the weights along the path from {{mvar|i}} to {{mvar|j}} in  {{mvar|T}}

For this case, {{mvar|M}} is called an additive matrix and {{mvar|T}} is called an additive tree. Below we can see an example of an additive distance matrix and its corresponding tree:

[[File:Additive_distance_matrix.png|444x444px|Additive distance matrix (left) and its phylogeny tree (right)|center|frameless]]