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<div><h1>MutableMatrix -- the class of all mutable matrices</h1>
<div class="single"><h2>Description</h2>
<div>A mutable matrix in Macaulay2 is a rectangular array of elements of a specific ring, whose entries can be modified.<p/>
A mutable matrix is different from a <a href="___Matrix.html" title="the class of all matrices">Matrix</a> in that a matrix contains degree information for the target and source of the matrix, while a mutable matrix has no such information. Also, more operations are provided for matrices.<p/>
For an overview of mutable matrices, see <a href="_mutable_spmatrices.html" title="">mutable matrices</a>.<p/>
Mutable matrices can either be encoded in a sparse manner (the matrix only encodes the non-zero elements), or in a dense manner (all elements are stored -- even zeros). The distinction is an option to several of the routines that create mutable matrices (<a href="_mutable__Matrix.html" title="make a mutable matrix">mutableMatrix</a>, <a href="_mutable__Identity_lp__Ring_cm__Z__Z_rp.html" title="make a mutable identity matrix">mutableIdentity</a>). Certain operations over RR or CC are performed using the lapack library and require dense encoding of matrices: <a href="___L__Udecomposition.html" title="LU decomposition">LUdecomposition</a>, <a href="___S__V__D.html" title="singular value decomposition of a matrix">SVD</a>, <a href="_solve.html" title="solve a linear equation">solve</a>, <a href="_eigenvalues.html" title="find eigenvalues of a matrix">eigenvalues</a>, <a href="_eigenvectors.html" title="find eigenvectors of a matrix over RR or CC">eigenvectors</a>.<h3>row and column operations</h3>
<ul><li><span><a href="_row__Add.html" title="add a multiple of one row to another">rowAdd</a> -- add a multiple of one row to another</span></li>
<li><span><a href="_row__Swap.html" title="interchange rows">rowSwap</a> -- interchange rows</span></li>
<li><span><a href="_row__Permute.html" title="permute some rows">rowPermute</a> -- permute some rows</span></li>
<li><span><a href="_row__Mult.html" title="multiply a row by a ring element">rowMult</a> -- multiply a row by a ring element</span></li>
<li><span><a href="_column__Add.html" title="add a multiple of one column to another">columnAdd</a> -- add a multiple of one column to another</span></li>
<li><span><a href="_column__Swap.html" title="interchange columns">columnSwap</a> -- interchange columns</span></li>
<li><span><a href="_column__Permute.html" title="permute some columns">columnPermute</a> -- permute some columns</span></li>
<li><span><a href="_column__Mult.html" title="multiply a column by a ring element">columnMult</a> -- multiply a column by a ring element</span></li>
</ul>
<h3>matrix arithmetic</h3>
Many matrix arithmetic routines are only available for immutabie matrices, not mutable matrices. It is necessary to use <a href="_matrix.html" title="make a matrix">matrix</a> to make an immutable matrix first.</div>
</div>
<div class="waystouse"><h2>Functions and methods returning a mutable matrix :</h2>
<ul><li><span>mutableIdentity, see <span><a href="_mutable__Identity_lp__Ring_cm__Z__Z_rp.html" title="make a mutable identity matrix">mutableIdentity(Ring,ZZ)</a> -- make a mutable identity matrix</span></span></li>
<li><span><a href="_mutable__Matrix.html" title="make a mutable matrix">mutableMatrix</a> -- make a mutable matrix</span></li>
<li><span>randomMutableMatrix, see <span><a href="_random__Mutable__Matrix_lp__Z__Z_cm__Z__Z_cm__R__R_cm__Z__Z_rp.html" title="a random mutable matrix of integers">randomMutableMatrix(ZZ,ZZ,RR,ZZ)</a> -- a random mutable matrix of integers</span></span></li>
</ul>
<h2>Methods that use a mutable matrix :</h2>
<ul><li><span>MutableMatrix * MutableMatrix, see <span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span>RingElement * MutableMatrix, see <span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span>MutableMatrix + MutableMatrix, see <span><a href="__pl.html" title="a unary or binary operator, usually used for addition">+</a> -- a unary or binary operator, usually used for addition</span></span></li>
<li><span>- MutableMatrix, see <span><a href="_-.html" title="a unary or binary operator, usually used for negation or subtraction">-</a> -- a unary or binary operator, usually used for negation or subtraction</span></span></li>
<li><span>MutableMatrix - MutableMatrix, see <span><a href="_-.html" title="a unary or binary operator, usually used for negation or subtraction">-</a> -- a unary or binary operator, usually used for negation or subtraction</span></span></li>
<li><span>MutableMatrix == MutableMatrix, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>MutableMatrix == ZZ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ZZ == MutableMatrix, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>clean(RR,MutableMatrix), see <span><a href="_clean.html" title="Set to zero elements that are approximately zero">clean</a> -- Set to zero elements that are approximately zero</span></span></li>
<li><span>columnAdd(MutableMatrix,ZZ,Number,ZZ), see <span><a href="_column__Add.html" title="add a multiple of one column to another">columnAdd</a> -- add a multiple of one column to another</span></span></li>
<li><span>columnAdd(MutableMatrix,ZZ,RingElement,ZZ), see <span><a href="_column__Add.html" title="add a multiple of one column to another">columnAdd</a> -- add a multiple of one column to another</span></span></li>
<li><span>columnMult(MutableMatrix,ZZ,Number), see <span><a href="_column__Mult.html" title="multiply a column by a ring element">columnMult</a> -- multiply a column by a ring element</span></span></li>
<li><span>columnMult(MutableMatrix,ZZ,RingElement), see <span><a href="_column__Mult.html" title="multiply a column by a ring element">columnMult</a> -- multiply a column by a ring element</span></span></li>
<li><span>columnPermute(MutableMatrix,ZZ,List), see <span><a href="_column__Permute.html" title="permute some columns">columnPermute</a> -- permute some columns</span></span></li>
<li><span>columnSwap(MutableMatrix,ZZ,ZZ), see <span><a href="_column__Swap.html" title="interchange columns">columnSwap</a> -- interchange columns</span></span></li>
<li><span>eigenvalues(MutableMatrix), see <span><a href="_eigenvalues.html" title="find eigenvalues of a matrix">eigenvalues</a> -- find eigenvalues of a matrix</span></span></li>
<li><span>eigenvectors(MutableMatrix), see <span><a href="_eigenvectors.html" title="find eigenvectors of a matrix over RR or CC">eigenvectors</a> -- find eigenvectors of a matrix over RR or CC</span></span></li>
<li><span>entries(MutableMatrix), see <span><a href="_entries.html" title="lists the entries of a matrix">entries</a> -- lists the entries of a matrix</span></span></li>
<li><span>fillMatrix(MutableMatrix), see <span><a href="_fill__Matrix.html" title="fill a mutable matrix with random numbers">fillMatrix</a> -- fill a mutable matrix with random numbers</span></span></li>
<li><span>fillMatrix(MutableMatrix,ZZ), see <span><a href="_fill__Matrix.html" title="fill a mutable matrix with random numbers">fillMatrix</a> -- fill a mutable matrix with random numbers</span></span></li>
<li><span>LLL(MutableMatrix), see <span><a href="../../LLLBases/html/___L__L__L.html" title="compute an LLL basis">LLL</a> -- compute an LLL basis</span></span></li>
<li><span>LUdecomposition(MutableMatrix), see <span><a href="___L__Udecomposition.html" title="LU decomposition">LUdecomposition</a> -- LU decomposition</span></span></li>
<li><span>MutableMatrix _ Sequence, see <span><a href="___Matrix_sp_us_sp__Sequence.html" title="get entry of matrix">Matrix _ Sequence</a> -- get entry of matrix</span></span></li>
<li><span><a href="_matrix_lp__Mutable__Matrix_rp.html" title="make a matrix from a mutable one">matrix(MutableMatrix)</a> -- make a matrix from a mutable one</span></li>
<li><span>mutableMatrix(MutableMatrix), see <span><a href="_mutable__Matrix.html" title="make a mutable matrix">mutableMatrix</a> -- make a mutable matrix</span></span></li>
<li><span><a href="___Mutable__Matrix_sp_us_sp__Sequence_sp_eq_sp__Thing.html" title="assignment to an element of a mutable matrix">MutableMatrix _ Sequence = Thing</a> -- assignment to an element of a mutable matrix</span></li>
<li><span>norm(InexactField,MutableMatrix), see <span><a href="_norm.html" title="">norm</a></span></span></li>
<li><span>norm(MutableMatrix), see <span><a href="_norm.html" title="">norm</a></span></span></li>
<li><span>norm(RR,MutableMatrix), see <span><a href="_norm.html" title="">norm</a></span></span></li>
<li><span>numColumns(MutableMatrix), see <span><a href="_num__Columns_lp__Matrix_rp.html" title="number of columns in a matrix or mutable matrix">numColumns(Matrix)</a> -- number of columns in a matrix or mutable matrix</span></span></li>
<li><span>numRows(MutableMatrix), see <span><a href="_num__Rows_lp__Matrix_rp.html" title="number of rows in a matrix or mutable matrix">numRows(Matrix)</a> -- number of rows in a matrix or mutable matrix</span></span></li>
<li><span>precision(MutableMatrix), see <span><a href="_precision.html" title="">precision</a></span></span></li>
<li><span>ring(MutableMatrix), see <span><a href="_ring.html" title="get the associated ring of an object">ring</a> -- get the associated ring of an object</span></span></li>
<li><span>rowAdd(MutableMatrix,ZZ,Number,ZZ), see <span><a href="_row__Add.html" title="add a multiple of one row to another">rowAdd</a> -- add a multiple of one row to another</span></span></li>
<li><span>rowAdd(MutableMatrix,ZZ,RingElement,ZZ), see <span><a href="_row__Add.html" title="add a multiple of one row to another">rowAdd</a> -- add a multiple of one row to another</span></span></li>
<li><span>rowMult(MutableMatrix,ZZ,Number), see <span><a href="_row__Mult.html" title="multiply a row by a ring element">rowMult</a> -- multiply a row by a ring element</span></span></li>
<li><span>rowMult(MutableMatrix,ZZ,RingElement), see <span><a href="_row__Mult.html" title="multiply a row by a ring element">rowMult</a> -- multiply a row by a ring element</span></span></li>
<li><span>rowPermute(MutableMatrix,ZZ,List), see <span><a href="_row__Permute.html" title="permute some rows">rowPermute</a> -- permute some rows</span></span></li>
<li><span>rowSwap(MutableMatrix,ZZ,ZZ), see <span><a href="_row__Swap.html" title="interchange rows">rowSwap</a> -- interchange rows</span></span></li>
<li><span>solve(MutableMatrix,MutableMatrix), see <span><a href="_solve.html" title="solve a linear equation">solve</a> -- solve a linear equation</span></span></li>
<li><span>SVD(MutableMatrix), see <span><a href="___S__V__D.html" title="singular value decomposition of a matrix">SVD</a> -- singular value decomposition of a matrix</span></span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Mutable__Matrix.html" title="the class of all mutable matrices">MutableMatrix</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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