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<head><title>exterior power of a matrix</title>
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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_matrices.html" title="">matrices</a> > <a href="_exterior_sppower_spof_spa_spmatrix.html" title="">exterior power of a matrix</a></div>
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<div><h1>exterior power of a matrix</h1>
<div>Since the <tt>i</tt>-th exterior power is a functor, it applies to matrices as well as to modules.<table class="examples"><tr><td><pre>i1 : R = ZZ[vars(0..19)]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : ff = genericMatrix(R,4,5)
o2 = | a e i m q |
| b f j n r |
| c g k o s |
| d h l p t |
4 5
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : exteriorPower (2,ff)
o3 = | -be+af -bi+aj -fi+ej -bm+an -fm+en -jm+in -bq+ar -fq+er -jq+ir -nq+mr
| -ce+ag -ci+ak -gi+ek -cm+ao -gm+eo -km+io -cq+as -gq+es -kq+is -oq+ms
| -cf+bg -cj+bk -gj+fk -cn+bo -gn+fo -kn+jo -cr+bs -gr+fs -kr+js -or+ns
| -de+ah -di+al -hi+el -dm+ap -hm+ep -lm+ip -dq+at -hq+et -lq+it -pq+mt
| -df+bh -dj+bl -hj+fl -dn+bp -hn+fp -ln+jp -dr+bt -hr+ft -lr+jt -pr+nt
| -dg+ch -dk+cl -hk+gl -do+cp -ho+gp -lo+kp -ds+ct -hs+gt -ls+kt -ps+ot
------------------------------------------------------------------------
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6 10
o3 : Matrix R <--- R</pre>
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Note that each entry of in the above matrix is a <tt>2</tt> by <tt>2</tt> minor (the determinant of a <tt>2</tt> by <tt>2</tt> submatrix) of the matrix <tt>ff</tt>.</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_exterior_sppower_spof_spa_spmodule.html" title="">exterior power of a module</a></span></li>
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