Reduced Form
A Latin square is said to be reduced (also, normalized or in standard form) if both its first row and its first column are in their natural order. For example, the above Latin square is not reduced because its first column is A, C, B rather than A, B, C.
We can make any Latin square reduced by permuting (reordering) the rows and columns. Here switching the above matrix's second and third rows yields
| A | B | C |
| B | C | A |
| C | A | B |
which is reduced: Both its first row and its first column are alphabetically ordered A, B, C.
Read more about this topic: Latin Square
Famous quotes containing the words reduced and/or form:
“The Gettysburg speech is at once the shortest and the most famous oration in American history. Put beside it, all the whoopings of the Websters, Sumners and Everetts seem gaudy and silly. It is eloquence brought to a pellucid and almost gem-like perfection—the highest emotion reduced to a few poetical phrases.”
—H.L. (Henry Lewis)
“Ambivalence reaches the level of schizophrenia in our treatment of violence among the young. Parents do not encourage violence, but neither do they take up arms against the industries which encourage it. Parents hide their eyes from the books and comics, slasher films, videos and lyrics which form the texture of an adolescent culture. While all successful societies have inhibited instinct, ours encourages it. Or at least we profess ourselves powerless to interfere with it.”
—C. John Sommerville (20th century)