Compound matrix: Difference between revisions

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{{unreferenced|date=August 2012}}

In mathematics, the ''k''th '''compound matrix''' <math>C_k(A)</math>,<ref>R.A. Horn and C.R. Johnson, ''Matrix Analysis'', Cambridge University Press, 1990, pp. 19–20</ref> of an <math>m\times n</math> [[matrix (mathematics)|matrix]] ''A'' is the <math>\binom m k\times \binom n k</math> matrix formed from the [[determinant]]s of all <math> k\times k</math> submatrices of ''A'', i.e., all <math>k\times k</math> minors, arranged with the submatrix index sets in [[lexicographic order]].

In mathematics, the ''k''th '''compound matrix''' <math>C_k(A)</math>,

<ref>R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, 1990, pp. 19-20</ref>

of an <math>m\times n</math> [[matrix (mathematics)|matrix]] ''A'' is the <math>\binom m k\times \binom n k</math> matrix formed from the [[determinant]]s of all <math> k\times k</math> submatrices of ''A'', i.e., all <math>k\times k</math> minors,

arranged with the submatrix index sets in [[lexicographic order]].

: <math>

\begin{align}

Line 17 ⟶ 14:

\end{align}

</math>

== See also ==

To efficiently calculate compound matrices see:

[http://users.uoa.gr/~mmitroul/mmitroulweb/numalg09.pdf "Compound matrices: properties, numerical issues and analytical computations" - Christos Kravvaritis · Marilena Mitrouli - DOI 10.1007/s11075-008-9222-7]

==References==

{{reflist}}

2. Gantmacher, F. R. and Krein, M. G. "Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems", Revised Edition, http://www.ams.org/bookstore?fn=20&arg1=diffequ&ikey=CHEL-345-H

==External links==

2.* Gantmacher, F. R. and Krein, M. G., "''Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems"'', Revised Edition, http://www.ams.org/bookstore?fn=20&arg1=diffequ&ikey=CHEL-345-H

* To efficiently calculate compound matrices see: [http://users.uoa.gr/~mmitroul/mmitroulweb/numalg09.pdf "Compound matrices: properties, numerical issues and analytical computations" - Christos Kravvaritis · Marilena Mitrouli - DOI 10.1007/s11075-008-9222-7]

[[Category:Matrices]]