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Difference between revisions of "Submatrix"

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[[Category:Linear and multilinear algebra; matrix theory]]
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{{MSC|15Axx|}}
 
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''of a matrix $A$ of dimension $m\times n$''
 
''of a matrix $A$ of dimension $m\times n$''
  
A matrix of dimension $k\times l$, where $1<k<m$, $1<l<n$, formed by the elements at the intersection of $k$ specified rows and $l$ specified columns of $A$ with retention of the previous order. The determinant of a square submatrix of order $k$ of a matrix $A$ is called a minor of order $k$ of $A$.
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A matrix of dimension $k\times l$, where $1<k<m$, $1<l<n$, formed by the elements at the intersection of $k$ specified rows and $l$ specified columns of $A$ with retention of the previous order. The determinant of a square submatrix of order $k$ of a matrix $A$ is called a ''[[minor]]'' of order $k$ of $A$.

Latest revision as of 19:36, 11 December 2015

2010 Mathematics Subject Classification: Primary: 15Axx [MSN][ZBL]

of a matrix $A$ of dimension $m\times n$

A matrix of dimension $k\times l$, where $1<k<m$, $1<l<n$, formed by the elements at the intersection of $k$ specified rows and $l$ specified columns of $A$ with retention of the previous order. The determinant of a square submatrix of order $k$ of a matrix $A$ is called a minor of order $k$ of $A$.

How to Cite This Entry:
Submatrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Submatrix&oldid=29511
This article was adapted from an original article by T.S. Pigolkina (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article