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Excel's storage of numbers in binary format also affects its accuracy. [3] To illustrate, the lower figure tabulates the simple addition 1 + x − 1 for several values of x. All the values of x begin at the 15 th decimal, so Excel must take them into account. Before calculating the sum 1 + x, Excel first approximates x as a binary number
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".
If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form (row value, column value). [ 4 ] One can similarly define the Cartesian product of n sets, also known as an n -fold Cartesian product , which can be represented by an n -dimensional array, where each element is an n - tuple .
Matrix multiplication shares some properties with usual multiplication. However, matrix multiplication is not defined if the number of columns of the first factor differs from the number of rows of the second factor, and it is non-commutative, [10] even when the product remains defined after changing the order of the factors. [11] [12]
Interchanging two rows or two columns affects the determinant by multiplying it by −1. [36] Using these operations, any matrix can be transformed to a lower (or upper) triangular matrix, and for such matrices, the determinant equals the product of the entries on the main diagonal; this provides a method to calculate the determinant of any matrix.
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
During the multiplication phase, the lattice is filled in with two-digit products of the corresponding digits labeling each row and column: the tens digit goes in the top-left corner. During the addition phase, the lattice is summed on the diagonals.
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.