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Sun Creator (talk | contribs) m General fixes, typo(s) fixed: Therefore → Therefore, |
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Taking the {{math|''r''}}th exterior power of this linear transformation determines a linear transformation
:<math>\wedge^r A \colon \wedge^r \mathbf{R}^n \to \wedge^r \mathbf{R}^m.</math>
The matrix corresponding to this linear transformation (with respect to the above bases of the exterior powers) is {{math|''C''<sub>''r''</sub>(''A'')}}. Taking exterior powers is a [[functor]], which means that<ref>Joseph P.S. Kung, Gian-Carlo Rota, and [[Catherine Yan|Catherine H. Yan]], ''[[Combinatorics:
:<math>\wedge^r (AB) = (\wedge^r A)(\wedge^r B).</math>
This corresponds to the formula {{math|1=''C''<sub>''r''</sub>(''AB'') = ''C''<sub>''r''</sub>(''A'')''C''<sub>''r''</sub>(''B'')}}. It is closely related to, and is a strengthening of, the [[Cauchy–Binet formula]].
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