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Swapping two rows, Multiplying a row by a nonzero number, Adding a multiple of one row to another row. Using these operations, a matrix can always be transformed into an upper triangular matrix (possibly bordered by rows or columns of zeros), and in fact one that is in row echelon form.
In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144 ...
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".
Napier then constructs a third table of proportions with 69 columns and 21 rows, which he calls his "radical table." [1]: p. 35 The proportion along the top rows, starting with 1 is 0.99. The entries in each column are in proportion 0.9995. (Note that 0.9995 = 1-1/2000, allowing "tolerably easy" multiplication by halving, shifting and ...
A variant called rook pivoting at each step involves search of maximum element the way rook moves on a chessboard, along column, row, column again and so on till reaching a pivot maximal in both its row and column. It can be proven that for large matrices of random elements its cost of operations at each step is similarly to partial pivoting ...
On paper, write down in one column the numbers you get when you repeatedly halve the multiplier, ignoring the remainder; in a column beside it repeatedly double the multiplicand. Cross out each row in which the last digit of the first number is even, and add the remaining numbers in the second column to obtain the product.
The goal is to select a subset of the rows such that the digit 1 appears in each column exactly once. Algorithm X works as follows: If the matrix A has no columns, the current partial solution is a valid solution; terminate successfully.
tells maximum number of columns Y rows tells maximum number of rows; C record Use: Cell contents; Record type: C; Mandatory fields: X column column position (one based) Possible fields: Y row row position (one based). If omitted, most recently encountered value is used. E expression expression for the cell K value value of the cell C column ...