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A spreadsheet consists of a table of cells arranged into rows and columns and referred to by the X and Y locations. X locations, the columns, are normally represented by letters, "A," "B," "C," etc., while rows are normally represented by numbers, 1, 2, 3, etc. A single cell can be referred to by addressing its row and column, "C10".
Thus, each row of a right stochastic matrix (or column of a left stochastic matrix) is a probability vector. Right stochastic matrices act upon row vectors of probabilities by multiplication from the right (hence their name) and the matrix entry in the i-th row and j-th column is the probability of transition from state i to state j.
Note that although cell C is in column 2, C is the 1st cell declared in row 3, because column 1 is occupied by cell A, which was declared in row 2. Cell G is the only cell declared in row 5, because cell F occupies the other columns but was declared in row 4.
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Edit-tricks are most useful when multiple tables must be changed, then the time needed to develop complex edit-patterns can be applied to each table. For each table, insert an alpha-prefix on each column (making each row-token "|-" to sort as column zero, like prefix "Row124col00"), then sort into a new file, and then de-prefix the column entries.
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A row can be replaced by the sum of that row and a multiple of another row. R i + k R j → R i , where i ≠ j {\displaystyle R_{i}+kR_{j}\rightarrow R_{i},{\mbox{where }}i\neq j} If E is an elementary matrix, as described below, to apply the elementary row operation to a matrix A , one multiplies A by the elementary matrix on the left, EA .