Submatrix

A submatrix is a matrix obtained starting from a matrix by keeping only certain lines or columns.

For example

A=\begin{pmatrix} a_ {11} & a_ {12} & a_ {13} & a_ {14} \ \ a_ {21} & a_ {22} & a_ {23} & a_ {24} \ \ a_ {31} & a_ {32} & a_ {33} & a_ {34} \end{pmatrix} Then
A_ {\ {1,2 \} \ {1,3,4 \}} = \ begin {pmatrix} a_ {11} & a_ {13} & a_ {14} \ \ a_ {21} & a_ {23} & a_ {24} \end{pmatrix} is a submatrix of has consisted of lines 1 and 2, and columns 1,3 and 4. We can also say that this submatrix is formed in removing line 3 and column 2.

There is no notation standardized to indicate a submatrix - also conventions of notations will be always specified.

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