Submatrix

Dependencies:

Let $A$ be a matrix. A submatrix of $A$ is a matrix obtained by removing certain rows and/or columns from $A$.

The submatrix $A_{S, T}$ or $A[S, T]$ is the matrix obtained by keeping only the rows which are in $S$ and columns which are in $T$.
The submatrix $A_{i_1..i_2, j_1..j_2}$ or $A[i_1..i_2, j_1..j_2]$ is the matrix obtained by keeping only the rows numbered from $i_1$ to $i_2$ and columns numbered from $j_1$ to $j_2$.
The submatrix $A_{-S, -T}$ or $A[-S, -T]$ or $A_{\backslash S, \backslash T}$ or $A[\backslash S, \backslash T]$ is the matrix obtained by removing rows which are in $S$ and columns which are in $T$.
The submatrix $A_{-i, -j}$ or $A[-i, -j]$ or $A_{\backslash i, \backslash j}$ or $A[\backslash i, \backslash j]$ is the matrix obtained by removing the $i^{\textrm{th}}$ row and $j^{\textrm{th}}$ column from $A$.