Matrices: indexing, row and column sums

Real data is usually two-dimensional: a grid of rows and columns. A spreadsheet, a feature table, a grayscale image — all are matrices, and in plain Python a matrix is a list whose elements are themselves lists. Each inner list is one row:

M = [[1, 2, 3],
     [4, 5, 6]]

To reach a single cell you index twice — row first, then column — the same convention mathematics uses:

print(M[0][2])   # row 0, column 2 -> 3
print(M[1][0])   # row 1, column 0 -> 4

Two dimensions mean two loops, one inside the other. Summing each row is a loop over rows, where each row is itself something you can sum:

for row in M:
    print(sum(row))      # 6, then 15

Summing each column is subtler, because a column runs across the rows. You hold a column index fixed and loop down the rows:

ncols = len(M[0])
for c in range(ncols):
    col_total = 0
    for r in range(len(M)):
        col_total += M[r][c]
    print(col_total)     # 5, 7, 9

That outer-then-inner nested loop is the grammar of all 2-D work.
leads into “Transpose and the ragged-row pitfalls”.*