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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_matrices.html" title="">matrices</a> > <a href="_determinants_spand_spminors.html" title="">determinants and minors</a></div>
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<div><h1>determinants and minors</h1>
<div>The command <a href="_determinant.html" title="determinant of a matrix">determinant</a> can be used to compute the determinant of a square matrix.<table class="examples"><tr><td><pre>i1 : R = ZZ[a..d];</pre>
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<tr><td><pre>i2 : f = matrix{{a,b},{c,d}}
o2 = | a b |
| c d |
2 2
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : det f
o3 = - b*c + a*d
o3 : R</pre>
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The command <a href="_minors_lp__Z__Z_cm__Matrix_rp.html" title="ideal generated by minors">minors</a> can be used to construct the ideal generated by the <tt>n</tt> by <tt>n</tt> minors of a matrix. Recall that the <tt>n</tt> by <tt>n</tt> minors of a matrix are the determinants of the <tt>n</tt> by <tt>n</tt> submatrices of a matrix.<table class="examples"><tr><td><pre>i4 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i5 : f = matrix{{x,y,z},{y,z,x^2}}
o5 = | x y z |
| y z x2 |
2 3
o5 : Matrix R <--- R</pre>
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<tr><td><pre>i6 : I = minors(2,f)
2 3 2 2
o6 = ideal (- y + x*z, x - y*z, x y - z )
o6 : Ideal of R</pre>
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