3

I have some large matrices, which I need to remove the first row and first column (both of which are full of zeroes). In this sense I need the inverse of "ArrayPad".

For example, consider the matrix:

A = {{0, 0, 0, 0}, {0, 1, 2, 3}, {0, 4, 5, 6} , {0, 7, 8, 9}}
A // MatrixForm

I would like an operation to reduce it to

Anew =  {{1, 2, 3}, {4, 5, 6} , {7, 8, 9}}
Anew // MatrixForm

I need general recipe for such operation for to go from (N+1) by (N+1) matrix to N by N matrix by removing the first column of zeroes and first row of zeroes.

Any help appreciated.

Nigel1
  • 773
  • 4
  • 10

3 Answers3

4

Rest is the built-in function for removing the first element from a list, so given 

m = {{0, 0, 0, 0}, {0, 1, 2, 3}, {0, 4, 5, 6}, {0, 7, 8, 9}};

then

Rest[Rest /@ m]

produces

{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}

as does

Rest /@ Rest[m]
m_goldberg
  • 107,779
  • 16
  • 103
  • 257
4
m0 =  {{1,2,3},{4,5,6},{7,8,9}};
m1 = ArrayPad[m0, {{1,0},{1,0}}]

{{0,0,0,0}, {0,1,2,3},{0,4,5,6},{0, 7,8,9}}

m2 = ArrayPad[m1, -{{1,0},{1, 0}}]

{{1,2,3},{4,5,6},{7,8,9}}

kglr
  • 394,356
  • 18
  • 477
  • 896
3

You can use the [[ ]] notation, which is backed by Part. You just need to start from an index of 2. i.e.

A[[2 ;;, 2 ;;]]

For example, if we have a matrix x given by

x = Table[j + 4 i + 1, {i, 0, 3}, {j, 0, 3}];
x // MatrixForm

$\left( \begin{array}{cccc} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 14 & 15 & 16 \\ \end{array} \right)$

Then the operation

x[[2 ;;, 2 ;;]]

gives

% // MatrixForm

$\left( \begin{array}{ccc} 6 & 7 & 8 \\ 10 & 11 & 12 \\ 14 & 15 & 16 \\ \end{array} \right)$

Lucas
  • 828
  • 4
  • 14