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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_matrices.html" title="">matrices</a> > <a href="_extracting_spinformation_spabout_spa_spmatrix.html" title="">extracting information about a matrix</a></div>
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<div><h1>extracting information about a matrix</h1>
<div>Consider the ring <tt>R</tt> and the matrix <tt>f</tt>.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : f = matrix{{2,x,y,x^2},{z,32,2,x}}
o2 = | 2 x y x2 |
| z 32 2 x |
2 4
o2 : Matrix R <--- R</pre>
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<h2>target</h2>
From the above output, one sees that Macaulay2 considers <tt>f</tt> as a linear transformation. Use the <a href="_target.html" title="target of a map">target</a> command to obtain the target of the linear transformation <tt>f</tt>.<table class="examples"><tr><td><pre>i3 : target f
2
o3 = R
o3 : R-module, free</pre>
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<h2>source</h2>
Likewise, to obtain the source of our linear transformation, use the <a href="_source.html" title="source of a map">source</a> command.<table class="examples"><tr><td><pre>i4 : source f
4
o4 = R
o4 : R-module, free, degrees {1, 1, 1, 2}</pre>
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<h2>number of rows or columns</h2>
Use <a href="_numgens.html" title="the number of generators">numgens</a> to obtain the rank of a free module. Combining it with the commands <a href="_target.html" title="target of a map">target</a> or <a href="_source.html" title="source of a map">source</a> gives us a way to determine the number of rows or columns of a matrix <tt>f</tt>.<table class="examples"><tr><td><pre>i5 : numgens target f
o5 = 2</pre>
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<tr><td><pre>i6 : numgens source f
o6 = 4</pre>
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<h2>extracting an element from a matrix</h2>
To extract the <tt>(i,j)</tt>-th element of a matrix, type <tt>f_(i,j)</tt>.<table class="examples"><tr><td><pre>i7 : f_(1,3)
o7 = x
o7 : R</pre>
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Note that the first number selects the row, starting at <tt>0</tt> and the second number selects the column, also starting at <tt>0</tt>.<h2>entries of a matrix</h2>
To obtain the entries of a matrix in the form of a list of lists, use the <a href="_entries.html" title="lists the entries of a matrix">entries</a> command.<table class="examples"><tr><td><pre>i8 : entries f
2
o8 = {{2, x, y, x }, {z, 32, 2, x}}
o8 : List</pre>
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Note that each inner list is a list of elements from a row of <tt>f</tt>.<h2>ring</h2>
The <a href="_ring.html" title="get the associated ring of an object">ring</a> command can be used to return the ring of the matrix, that is, the ring containing entries of the matrix.<table class="examples"><tr><td><pre>i9 : ring f
o9 = R
o9 : PolynomialRing</pre>
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Use the <a href="_describe.html" title="real description">describe</a> command to recover how the ring of <tt>f</tt> was constructed.<table class="examples"><tr><td><pre>i10 : describe ring f
o10 = QQ[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder =>
-----------------------------------------------------------------------
{MonomialSize => 32}, DegreeRank => 1]
{GRevLex => {3:1} }
{Position => Up }</pre>
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