Row-Major Matrix Indexing

Row-major matrix indexing

Row-major indexing means you read or store a matrix row by row: all entries in the first row come first, then all entries in the second row, and so on. To answer these exercises, you usually need to convert between a matrix position ((i,j)) and a single linear index.

1) Identify the matrix size

Count the number of columns first. In row-major order, the number of columns determines how many positions are covered by each row.

2) Convert a position to a linear index

If indexing starts at 0, use: [ \text{index} = i \times (\text{number of columns}) + j. ] If indexing starts at 1, adjust accordingly by subtracting 1 from the row and column first, then converting back if needed.

3) Convert a linear index to a position

Divide the index by the number of columns:

• the quotient gives the row,
• the remainder gives the column.

4) Simplify carefully

Keep arithmetic exact. If the exercise asks for an exact saved answer, do not round or approximate.

Check

Make sure the index is counted left to right within each row, then top to bottom across rows. A quick sanity check is that entries in the same row should have consecutive indices.