How do I drop the first/last row or first/last column from a matrix? The general case is answered here but I am new to Mathematica and it the arbitrary case is unnecessarily complex.
Suppose I am dealing with a 4 by 4 square matrix such as
m = Array[Subscript[a, ##] &, {4, 4}]
and would like to delete the first and last rows as well as columns.
This may involve a simple application of the drop function I reckon. I would appreciate a very barebones example.
Okay, following the "bare bones" approach for dropping rows and columns here are a few ideas.
Starting matrix:
m = Array[Times, {5, 6}]
$\left( \begin{array}{ccccc} 1 & 2 & 3 & 4 & 5 \\ 2 & 4 & 6 & 8 & 10 \\ 3 & 6 & 9 & 12 & 15 \\ 4 & 8 & 12 & 16 & 20 \\ \end{array} \right)$
When possible I use Part:
To "delete the last row and first column" we can use:
m[[;; -2, 2 ;;]]
$\left( \begin{array}{cccc} 2 & 3 & 4 & 5 \\ 4 & 6 & 8 & 10 \\ 6 & 9 & 12 & 15 \\ \end{array} \right)$
This uses Span. The specification for Part is in the order of rows, then columns, as this is how Mathematica arrays are composed. The first specification is:
;; -2
This is shorthand for 1 ;; -2 which means elements one through two from the end.
The second specification is:
2 ;;
This is shorthand for 2 ;; All which means elements two through the end.
For an abstraction of Part to simultaneously delete arbitrary rows and columns see:
Drop, while not capable of deleting arbitrary rows (or with effort, columns) like Delete, can accept an interval parameter (as can Part by way of Span) to e.g. drop every other element, and it can operate on rows and columns simultaneously like Part. An example of both:
Drop[m, None, {1, -1, 2}]
$\left( \begin{array}{cc} 2 & 4 \\ 4 & 8 \\ 6 & 12 \\ 8 & 16 \\ \end{array} \right)$
For the question application "delete the last row and first column" it is very concise:
Drop[m, -1, 1]
$\left( \begin{array}{cccc} 2 & 3 & 4 & 5 \\ 4 & 6 & 8 & 10 \\ 6 & 9 & 12 & 15 \\ \end{array} \right)$
You can also use Delete in many cases, however Delete does not support All like Part does which makes it less efficient for column operations, as as one must either Map the function or Transpose the array.
Delete[#, 1] & /@ Delete[m, -1]
$\left( \begin{array}{cccc} 2 & 3 & 4 & 5 \\ 4 & 6 & 8 & 10 \\ 6 & 9 & 12 & 15 \\ \end{array} \right)$
Delete[Delete[m, -1]\[Transpose], 1]\[Transpose]
$\left( \begin{array}{cccc} 2 & 3 & 4 & 5 \\ 4 & 6 & 8 & 10 \\ 6 & 9 & 12 & 15 \\ \end{array} \right)$
However unlike Drop it is not limited to starting, trailing, or evenly spaced elements and allow for e.g.:
Delete[m, {{1}, {3}}]
$\left( \begin{array}{ccccc} 2 & 4 & 6 & 8 & 10 \\ 4 & 8 & 12 & 16 & 20 \\ \end{array} \right)$
When you wish to work with columns it is easier and more efficient to use the Part abstraction referenced earlier.
A barebones example for the desired cropping is:
m = Array[Subscript[a, ##] &, {4, 4}];
MatrixForm[m]
$$\left( \begin{array}{cccc} a_{1,1} & a_{1,2} & a_{1,3} & a_{1,4} \\ a_{2,1} & a_{2,2} & a_{2,3} & a_{2,4} \\ a_{3,1} & a_{3,2} & a_{3,3} & a_{3,4} \\ a_{4,1} & a_{4,2} & a_{4,3} & a_{4,4} \\ \end{array} \right)$$
ArrayPad[m, {{0, -1}, {-1, 0}}]
$$\left( \begin{array}{ccc} a_{1,2} & a_{1,3} & a_{1,4} \\ a_{2,2} & a_{2,3} & a_{2,4} \\ a_{3,2} & a_{3,3} & a_{3,4} \\ \end{array} \right)$$
Here, I use the fact that ArrayPad permits zero or negative values of the padding, so one can use it to shrink matrices arbitrarily on all sides.
Also, slick way to do the cropping on all sides of a matrix is this:
ArrayPad[m, -1]
$$\left( \begin{array}{cc} a_{2,2} & a_{2,3} \\ a_{3,2} & a_{3,3} \\ \end{array} \right)$$
Seeing you asked about how to drop the first or last rows/columns, you can do that conveniently with Most and Rest:
Most@m (* drops last row *)
Most/@m (* drops last column *)
Rest@m (* drops first row *)
Rest/@m (* drops first column *)
