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Difference between revisions of "Submatrix"

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''of a matrix <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s0909301.png" /> of dimension <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s0909302.png" />''
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A matrix of dimension <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s0909303.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s0909304.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s0909305.png" />, formed by the elements at the intersection of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s0909306.png" /> specified rows and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s0909307.png" /> specified columns of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s0909308.png" /> with retention of the previous order. The determinant of a square submatrix of order <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s0909309.png" /> of a matrix <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s09093010.png" /> is called a minor of order <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s09093012.png" /> of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090930/s09093013.png" />.
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''of a matrix $A$ of dimension $m\times n$''
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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 $A$.

Revision as of 10:03, 5 March 2013


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://www.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