general linear group
Word Rarity
Uncommon
Frequency: Zipf frequency 4.09 in modern English
22
Scrabble Score
18
Letters
6
Syllables
10
Unique Chars
Meaning
noun
For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication.
Example Sentences
- "1993, Peter J. Olver, Applications of Lie Groups to Differential Equations, Springer, 2000, Softcover Reprint, page 17, Often Lie groups arise as subgroups of certain larger Lie groups; for example, the orthogonal groups are subgroups of the general linear groups of all invertible matrices."
- "We will again call this group the general linear group and denote it by GL₃. In just the same way, the set of all nonsingular linear transformations of the plane L₂ is a group denoted by GL₂ and called the general linear group of order two."
- "We show how to put a Lie group structure on a closed subgroup of the general linear group and determine the Lie algebras of the classical groups."