Rendering a matrix as a linear array

Rendering a matrix as a linear array is a procedure common in generations of programming languages predating Python. How do I convert between the index of the linear array and the coordinates row and column of the corresponding matrix?

Matrix showing linear array-indices of matrix-cells:

row_number: +—————————————————+
    2       | 8 | 9 | 10 | 11 |
            +———+———+————+————+
    1       | 4 | 5 |  6 |  7 |
            +———+———+————+————+
    0       | 0 | 1 |  2 |  3 |
            +—————————————————+
              0 | 1 |  2 |  3    <= column_number

  total_rows    = 3
  total_columns = 4

Three small calculations are needed to convert between an index and the corresponding row_number and column_number:

    index = row_number * total_columns + column_number
    column_number = index % total_columns
    # Python 3, non-integer division
    row_number = (index - column_number) / total_columns
    # Alternately, by integer division
    row_number = index // total_columns

As for "non-integer division", Guido van Rossum proposed "float division" for this: ([http://mail.python.org/pipermail/python-dev/2001-March/013444.html], 20010311, accessed 20130722)

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