Koofers

TESTBANK•PROF RATINGS•GPA HISTORIES•FLASHCARDS•SCHEDULES•TEXTBOOKS•DEALS
Universities » Cornell University (Cornell) » MATH - Mathematics » 4310 - Linear Algebra » Flash Cards

Groups and Geometry Prelim II - Flashcards

Flashcard Deck Information

Class:MATH 4310 - Linear Algebra
Subject:Mathematics
University:Cornell University
Term:Spring 2010
- of -
INCORRECT CORRECT
- INCORRECT     - CORRECT     - SKIPPED
Shuffle Remaining Cards Show Definitions First Take Quiz (NEW)
Hide Keyboard shortcuts
Next card
Previous card
Mark correct
Mark incorrect
Flip card
Start Over
Shuffle
      Mode:   CARDS LIST       ? pages   PRINT EXIT
Plato's Solids Regular convex polyhedrons. Only five exist: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
dual solids geometrical solids which have the same number and type of symmetries. - the cube and octahedron are dual: any symmetry of the cube is a symmetry of the octahedron.
Cayley's Theorem (wikipedia) Every group G is isomorphic to a subgroup of the symmetric group on G. - by extension, finite groups G of order n are isomorphic to a subgroup of Sn.
general linear group GLn(R): the set of n-by-n invertible matrices with entries from the real numbers. (matrix multiplication is associative, there is the n-by-n identity matrix, and only matrices with inverses are included)
Generated by Koofers.com
special linear group SLn(R): the set of n-by-n invertible matrices whose determinant is 1, with entries from the real numbers (the determinant of a product is the product of their determinants)
orthogonal matrix a matrix A such that (A^t)(A) = I. Its columns (or rows) are orthonormal (their dot products is zero and their lengths are one)
orthogonal group On(R): the set of invertible n-by-n matrices that are orthogonal with entries from the real numbers (det = +/- 1).
special orthogonal group SOn(R): the subgroup of orthogonal matrices with determinant 1 (the intersection of On and SLn)
Generated by Koofers.com

List View: Terms & Definitions

  Hide All 8 Print
 
Front
Back
 Plato's SolidsRegular convex polyhedrons. Only five exist: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
 dual solidsgeometrical solids which have the same number and type of symmetries. - the cube and octahedron are dual: any symmetry of the cube is a symmetry of the octahedron.
 Cayley's Theorem(wikipedia) Every group G is isomorphic to a subgroup of the symmetric group on G. - by extension, finite groups G of order n are isomorphic to a subgroup of Sn.
 general linear groupGLn(R): the set of n-by-n invertible matrices with entries from the real numbers. (matrix multiplication is associative, there is the n-by-n identity matrix, and only matrices with inverses are included)
 special linear groupSLn(R): the set of n-by-n invertible matrices whose determinant is 1, with entries from the real numbers (the determinant of a product is the product of their determinants)
 orthogonal matrixa matrix A such that (A^t)(A) = I. Its columns (or rows) are orthonormal (their dot products is zero and their lengths are one)
 orthogonal groupOn(R): the set of invertible n-by-n matrices that are orthogonal with entries from the real numbers (det = +/- 1).
 special orthogonal groupSOn(R): the subgroup of orthogonal matrices with determinant 1 (the intersection of On and SLn)
+0
Karma