Order of Matrix Groups
The general linear group of matrices of order m over Zn has order
The special linear group of matrices of order m over Zn has order
The symplectic group of matrices of order m over Zn has order
The first two formulas were discovered by Jordan.
Read more about this topic: Jordan's Totient Function
Famous quotes containing the words order, matrix and/or groups:
“The confusion of emotions with behavior causes no end of unnecessary trouble to both adults and children. Behavior can be commanded; emotions cant. An adult can put controls on a childs behaviorat least part of the timebut how do you put controls on what a child feels? An adult can impose controls on his own behaviorif hes grown upbut how does he order what he feels?”
—Leontine Young (20th century)
“As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”
—Margaret Atwood (b. 1939)
“If we can learn ... to look at the ways in which various groups appropriate and use the mass-produced art of our culture ... we may well begin to understand that although the ideological power of contemporary cultural forms is enormous, indeed sometimes even frightening, that power is not yet all-pervasive, totally vigilant, or complete.”
—Janice A. Radway (b. 1949)