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A submatrix is a matrix formed by taking certain rows and columns from a bigger matrix.
For example
- <math>
A=\begin{bmatrix}
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{bmatrix}
<math>
Then
- <math>
A[1,2; 1,3,4]=\begin{bmatrix}
a_{11} & a_{13} & a_{14} \\
a_{21} & a_{23} & a_{24}
\end{bmatrix}
<math>
is a submatrix of A formed by rows 1,2 and columns 1,3,4. This submatrix can also be denoted by A(3;2) which means that it is formed by deleting row 3 and column 2.
There is no standard way to denote a submatrix - although the above two methods are the most common - so one should be careful while reading an article on matrix theory.
The corresponding concept in determinant theory is of minor determinant, that is, determinant of a square submatrix.
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