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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Math-Algebra-LinearAlgebra.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>None</td></tr><tr><th>Language</th><td>Haskell98</td></tr></table><p class="caption">Math.Algebra.LinearAlgebra</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A module providing elementary operations involving scalars, vectors, and matrices
over a ring or field. Vectors are represented as [a], matrices as [[a]].
(No distinction is made between row and column vectors.)
It is the caller's responsibility to ensure that the lists have the correct number of elements.</p><p>The mnemonic for many of the arithmetic operations is that the number of angle brackets
on each side indicates the dimension of the argument on that side. For example,
v <*>> m is multiplication of a vector on the left by a matrix on the right.</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><a href="#v:-60--43--62-">(<+>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [a] -> [a]</li><li class="src short"><a href="#v:-60--45--62-">(<->)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [a] -> [a]</li><li class="src short"><a href="#v:-42--62-">(*>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => a -> [a] -> [a]</li><li class="src short"><a href="#v:-60-.-62-">(<.>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [a] -> a</li><li class="src short"><a href="#v:-60--42--62-">(<*>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [a] -> [[a]]</li><li class="src short"><a href="#v:-60--60--43--62--62-">(<<+>>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [[a]] -> [[a]] -> [[a]]</li><li class="src short"><a href="#v:-60--60--45--62--62-">(<<->>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [[a]] -> [[a]] -> [[a]]</li><li class="src short"><a href="#v:-60--60--42--62--62-">(<<*>>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [[a]] -> [[a]] -> [[a]]</li><li class="src short"><a href="#v:-42--62--62-">(*>>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => a -> [[a]] -> [[a]]</li><li class="src short"><a href="#v:-60--60--42--62-">(<<*>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [[a]] -> [a] -> [a]</li><li class="src short"><a href="#v:-60--42--62--62-">(<*>>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [[a]] -> [a]</li><li class="src short"><a href="#v:fMatrix">fMatrix</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Enum">Enum</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t1) => t1 -> (t1 -> t1 -> t) -> [[t]]</li><li class="src short"><a href="#v:fMatrix-39-">fMatrix'</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Enum">Enum</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t1) => t1 -> (t1 -> t1 -> t) -> [[t]]</li><li class="src short"><a href="#v:idMx">idMx</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> [[a]]</li><li class="src short"><a href="#v:iMx">iMx</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> [[t]]</li><li class="src short"><a href="#v:jMx">jMx</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> [[t]]</li><li class="src short"><a href="#v:zMx">zMx</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> [[t]]</li><li class="src short"><a href="#v:inverse">inverse</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a) => [[a]] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Maybe.html#t:Maybe">Maybe</a> [[a]]</li><li class="src short"><a href="#v:inverse1">inverse1</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> [[a]]</li><li class="src short"><a href="#v:inverse2">inverse2</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> [[a]]</li><li class="src short"><a href="#v:-33-">(!)</a> :: [a] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> a</li><li class="src short"><a href="#v:rowEchelonForm">rowEchelonForm</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> [[a]]</li><li class="src short"><a href="#v:reducedRowEchelonForm">reducedRowEchelonForm</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a) => [[a]] -> [[a]]</li><li class="src short"><a href="#v:solveLinearSystem">solveLinearSystem</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a) => [[a]] -> [a] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Maybe.html#t:Maybe">Maybe</a> [a]</li><li class="src short"><a href="#v:isZero">isZero</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Foldable.html#t:Foldable">Foldable</a> t) => t a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:inSpanRE">inSpanRE</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> [a] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:rank">rank</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a></li><li class="src short"><a href="#v:kernel">kernel</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a) => [[a]] -> [[a]]</li><li class="src short"><a href="#v:kernelRRE">kernelRRE</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a) => [[a]] -> [[a]]</li><li class="src short"><a href="#v:det">det</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a) => [[a]] -> a</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><a id="v:-60--43--62-" class="def">(<+>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [a] -> [a] <span class="fixity">infixl 6</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%3C%2B%3E" class="link">Source</a> <a href="#v:-60--43--62-" class="selflink">#</a></p><div class="doc"><p>u <+> v returns the sum u+v of vectors</p></div></div><div class="top"><p class="src"><a id="v:-60--45--62-" class="def">(<->)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [a] -> [a] <span class="fixity">infixl 6</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%3C-%3E" class="link">Source</a> <a href="#v:-60--45--62-" class="selflink">#</a></p><div class="doc"><p>u <-> v returns the difference u-v of vectors</p></div></div><div class="top"><p class="src"><a id="v:-42--62-" class="def">(*>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => a -> [a] -> [a] <span class="fixity">infixr 8</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%2A%3E" class="link">Source</a> <a href="#v:-42--62-" class="selflink">#</a></p><div class="doc"><p>k *> v returns the product k*v of the scalar k and the vector v</p></div></div><div class="top"><p class="src"><a id="v:-60-.-62-" class="def">(<.>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [a] -> a <span class="fixity">infixl 7</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%3C.%3E" class="link">Source</a> <a href="#v:-60-.-62-" class="selflink">#</a></p><div class="doc"><p>u <.> v returns the dot product of vectors (also called inner or scalar product)</p></div></div><div class="top"><p class="src"><a id="v:-60--42--62-" class="def">(<*>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [a] -> [[a]] <span class="fixity">infixl 7</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%3C%2A%3E" class="link">Source</a> <a href="#v:-60--42--62-" class="selflink">#</a></p><div class="doc"><p>u <*> v returns the tensor product of vectors (also called outer or matrix product)</p></div></div><div class="top"><p class="src"><a id="v:-60--60--43--62--62-" class="def">(<<+>>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [[a]] -> [[a]] -> [[a]] <span class="fixity">infixl 6</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%3C%3C%2B%3E%3E" class="link">Source</a> <a href="#v:-60--60--43--62--62-" class="selflink">#</a></p><div class="doc"><p>a <<+>> b returns the sum a+b of matrices</p></div></div><div class="top"><p class="src"><a id="v:-60--60--45--62--62-" class="def">(<<->>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [[a]] -> [[a]] -> [[a]] <span class="fixity">infixl 6</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%3C%3C-%3E%3E" class="link">Source</a> <a href="#v:-60--60--45--62--62-" class="selflink">#</a></p><div class="doc"><p>a <<->> b returns the difference a-b of matrices</p></div></div><div class="top"><p class="src"><a id="v:-60--60--42--62--62-" class="def">(<<*>>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [[a]] -> [[a]] -> [[a]] <span class="fixity">infixl 7</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%3C%3C%2A%3E%3E" class="link">Source</a> <a href="#v:-60--60--42--62--62-" class="selflink">#</a></p><div class="doc"><p>a <<*>> b returns the product a*b of matrices</p></div></div><div class="top"><p class="src"><a id="v:-42--62--62-" class="def">(*>>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => a -> [[a]] -> [[a]] <span class="fixity">infixr 8</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%2A%3E%3E" class="link">Source</a> <a href="#v:-42--62--62-" class="selflink">#</a></p><div class="doc"><p>k *>> m returns the product k*m of the scalar k and the matrix m</p></div></div><div class="top"><p class="src"><a id="v:-60--60--42--62-" class="def">(<<*>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [[a]] -> [a] -> [a] <span class="fixity">infixr 7</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%3C%3C%2A%3E" class="link">Source</a> <a href="#v:-60--60--42--62-" class="selflink">#</a></p><div class="doc"><p>m <<*> v is multiplication of a vector by a matrix on the left</p></div></div><div class="top"><p class="src"><a id="v:-60--42--62--62-" class="def">(<*>>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => [a] -> [[a]] -> [a] <span class="fixity">infixl 7</span><span class="rightedge"></span> <a href="src/Math-Algebra-LinearAlgebra.html#%3C%2A%3E%3E" class="link">Source</a> <a href="#v:-60--42--62--62-" class="selflink">#</a></p><div class="doc"><p>v <*>> m is multiplication of a vector by a matrix on the right</p></div></div><div class="top"><p class="src"><a id="v:fMatrix" class="def">fMatrix</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Enum">Enum</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t1) => t1 -> (t1 -> t1 -> t) -> [[t]] <a href="src/Math-Algebra-LinearAlgebra.html#fMatrix" class="link">Source</a> <a href="#v:fMatrix" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:fMatrix-39-" class="def">fMatrix'</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Enum">Enum</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t1) => t1 -> (t1 -> t1 -> t) -> [[t]] <a href="src/Math-Algebra-LinearAlgebra.html#fMatrix%27" class="link">Source</a> <a href="#v:fMatrix-39-" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:idMx" class="def">idMx</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> [[a]] <a href="src/Math-Algebra-LinearAlgebra.html#idMx" class="link">Source</a> <a href="#v:idMx" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:iMx" class="def">iMx</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> [[t]] <a href="src/Math-Algebra-LinearAlgebra.html#iMx" class="link">Source</a> <a href="#v:iMx" class="selflink">#</a></p><div class="doc"><p>iMx n is the n*n identity matrix</p></div></div><div class="top"><p class="src"><a id="v:jMx" class="def">jMx</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> [[t]] <a href="src/Math-Algebra-LinearAlgebra.html#jMx" class="link">Source</a> <a href="#v:jMx" class="selflink">#</a></p><div class="doc"><p>jMx n is the n*n matrix of all 1s</p></div></div><div class="top"><p class="src"><a id="v:zMx" class="def">zMx</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> [[t]] <a href="src/Math-Algebra-LinearAlgebra.html#zMx" class="link">Source</a> <a href="#v:zMx" class="selflink">#</a></p><div class="doc"><p>zMx n is the n*n matrix of all 0s</p></div></div><div class="top"><p class="src"><a id="v:inverse" class="def">inverse</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a) => [[a]] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Maybe.html#t:Maybe">Maybe</a> [[a]] <a href="src/Math-Algebra-LinearAlgebra.html#inverse" class="link">Source</a> <a href="#v:inverse" class="selflink">#</a></p><div class="doc"><p>The inverse of a matrix (over a field), if it exists</p></div></div><div class="top"><p class="src"><a id="v:inverse1" class="def">inverse1</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> [[a]] <a href="src/Math-Algebra-LinearAlgebra.html#inverse1" class="link">Source</a> <a href="#v:inverse1" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:inverse2" class="def">inverse2</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> [[a]] <a href="src/Math-Algebra-LinearAlgebra.html#inverse2" class="link">Source</a> <a href="#v:inverse2" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:-33-" class="def">(!)</a> :: [a] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> a <a href="src/Math-Algebra-LinearAlgebra.html#%21" class="link">Source</a> <a href="#v:-33-" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:rowEchelonForm" class="def">rowEchelonForm</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> [[a]] <a href="src/Math-Algebra-LinearAlgebra.html#rowEchelonForm" class="link">Source</a> <a href="#v:rowEchelonForm" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:reducedRowEchelonForm" class="def">reducedRowEchelonForm</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a) => [[a]] -> [[a]] <a href="src/Math-Algebra-LinearAlgebra.html#reducedRowEchelonForm" class="link">Source</a> <a href="#v:reducedRowEchelonForm" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:solveLinearSystem" class="def">solveLinearSystem</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a) => [[a]] -> [a] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Maybe.html#t:Maybe">Maybe</a> [a] <a href="src/Math-Algebra-LinearAlgebra.html#solveLinearSystem" class="link">Source</a> <a href="#v:solveLinearSystem" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:isZero" class="def">isZero</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Foldable.html#t:Foldable">Foldable</a> t) => t a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Math-Algebra-LinearAlgebra.html#isZero" class="link">Source</a> <a href="#v:isZero" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:inSpanRE" class="def">inSpanRE</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> [a] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Math-Algebra-LinearAlgebra.html#inSpanRE" class="link">Source</a> <a href="#v:inSpanRE" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:rank" class="def">rank</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a) => [[a]] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> <a href="src/Math-Algebra-LinearAlgebra.html#rank" class="link">Source</a> <a href="#v:rank" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:kernel" class="def">kernel</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a) => [[a]] -> [[a]] <a href="src/Math-Algebra-LinearAlgebra.html#kernel" class="link">Source</a> <a href="#v:kernel" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:kernelRRE" class="def">kernelRRE</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a) => [[a]] -> [[a]] <a href="src/Math-Algebra-LinearAlgebra.html#kernelRRE" class="link">Source</a> <a href="#v:kernelRRE" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:det" class="def">det</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Fractional">Fractional</a> a) => [[a]] -> a <a href="src/Math-Algebra-LinearAlgebra.html#det" class="link">Source</a> <a href="#v:det" class="selflink">#</a></p><div class="doc"><p>The determinant of a matrix (over a field)</p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.17.3</p></div></body></html>
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