View source for Determinant of Matrices with Integer Entries

{{DISPLAYTITLE:Determinant of Matrices with Integer Entries (Determinant of Matrices with Integer Entries)}}
== Description == 

Calculate the determinant of a given matrix with integer matrices. For such matrices, the determinant is also an integer.

== Parameters == 

<pre>n: dimension of matrix</pre>

== Table of Algorithms == 

{| class="wikitable sortable"  style="text-align:center;" width="100%"

! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference

|-

| [[Bareiss algorithm (Determinant of Matrices with Integer Entries Determinant of Matrices with Integer Entries)|Bareiss algorithm]] || 1968 || $O(n^{5}L^{2} (log(n)$^{2} + L^{2})) || $O(n^{2}(n*log(n)$+nL)) || Exact || Deterministic || [https://www-ams-org.ezproxy.canberra.edu.au/journals/mcom/1968-22-103/S0025-5718-1968-0226829-0/S0025-5718-1968-0226829-0.pdf Time]
|-
| [[Bareiss algorithm with fast multiplication (Determinant of Matrices with Integer Entries Determinant of Matrices with Integer Entries)|Bareiss algorithm with fast multiplication]] || 1968 || $O(n^{4}L(log(n)$ + L)log(log(n) + L)) || $O(n^{2}(n*log(n)$+nL)) || Exact || Deterministic ||  
|-
|}

== Time Complexity graph == 

[[File:Determinant of Matrices with Integer Entries - Time.png|1000px]]

== Space Complexity graph == 

[[File:Determinant of Matrices with Integer Entries - Space.png|1000px]]

== Pareto Decades graph == 

[[File:Determinant of Matrices with Integer Entries - Pareto Frontier.png|1000px]]