Extracting element(s) of a matrix : [] at

### 2.42.12 Extracting element(s) of a matrix : `[] at`

Recall that a matrix is a list of lists with same size.
Input :

`A:=[[3,4,5],[1,2,6]]`

Output :

`[[3,4,5],[1,2,6]]`

The prefixed function `at` or the index notation `[...]` is used to access to an element or a row or a column of a matrix:

- To extract an element, put the matrix and then, beetween square brackets put its row index, a comma, and its column index. In `Xcas` mode the first index is 0, in other modes the first index is 1.
  Input :
  `[[3,4,5],[1,2,6]][0,1]`
  or
  `A[0,1]`
  or
  `A[0][1]`
  or
  `at(A,[0,1])`
  Output :
  `4`
- To extract a row of the matrix `A`, put the matrix and then, beetween square brackets put the row index, input :
  `[[3,4,5],[1,2,6]][0]`
  or
  `A[0]`
  or
  `at(A,0)`
  Output :
  `[3,4,2]`
- To extract a part of a row, put two arguments beetween the square brackets : the row index and an interval to design the selected columns.
  Input :
  `A[1,0..2]`
  Output :
  `[1,2,6]`
  Input :
  `A[1,1..2]`
  Output :
  `[2,6]`
- To extract a column of the matrix `A`, first tranpose `A` (`transpose(A)`) then extract the row like above.
  Input :
  `tran(A)[1]`
  or
  `at(tran(A),1)`
  Output :
  `[4,2]`
- To extract a part of a column of the matrix `A` as a list, put two arguments beetween the square brackets : an index interval to design the selected rows and the column index.
  Input :
  `A[0..0,1]`
  Output :
  `[4]`

  This may be used to extract a full column, by specifying all the rows as index interval.
  Input :

  `A[0..1,1]`

  Output :

  `[4,2]`
- To extract a sub-matrix of a matrix, put between the square brackets two intervals : one interval for the selected rows and one interval for the selected columns.
  To definie the matrix `A`, input :
  `A:=[[3,4,5],[1,2,6]]`
  Input :
  `A[0..1,1..2]`
  Output :
  `[[4,5],[2,6]]`
  Input :
  `A[0..1,1..1]`
  Output :
  `[[4],[2]]`
  Remark If the second interval is omitted, the sub-matrix is made with the consecutive rows given by the first interval.
  Input :
  `A[1..1]`
  Output :
  `[[1,2,6]]`

You may also assign an element of a matrix using the index notation, if you assign with `:=` a new copy of the matrix is created and the element is modified, if you assign with `=<`, the matrix is modified in place.