John Stillwell - Naive Lie Theory.pdf - Index of

Index 213
in U(n), 65
introduced by Weyl, 72
Mercator, Nicholas, 141
Minkowski space, 113
Montgomery, Deane, 159
multiplicative notation, 24
multiplicative property
of absolute value, 6, 9, 20, 22
and isometries, 11
of determinants, 6, 9
of logarithm, 141, 146
of triangles, 18
neighborhood, 147, 162
topological, 149
Newton, Isaac, 141
Noether, Emmy, 117
nth roots of matrices, 144
O(3) is not path-connected, 186
O(n),48
definition, 51
is not path-connected, 52
octonion, 22
automorphisms, 45
projective plane, 22
open
ball, 161
interval, 163
set, 160, 162
in general topology, 162
sets, 161
orientation, 38, 50
and determinant, 38
preservation of, 38
reversal of, 38
orthogonal
complement
in M n (C), 148
of real quaternions, 12, 14
group, 48, 51
special, 3, 48, 51
matrix, 32, 97
transformation, 3, 49
vectors in R 3 ,13
orthonormal basis
of C n ,55
path, 94, 160
as a function, 173
as locus, 173
as orbit, 173
as sequence of positions, 52
closed, 178, 184
and simple connectivity,
178, 184
concatenation, 174
definition, 174
deformation of, 160
lifting, 179
smooth, 4, 114
definition, 93, 94
of matrices, 94
of quaternions, 79, 81
path-connectedness, 48, 52, 60,
160, 174
and center, 69
and concept of rotation, 52
of GL(n,C), 111, 175
of SL(n,C), 111
of SO(n), 52
of Sp(n), 57, 60
of SU(n), 56
of U(n), 69
Peano, Giuseppe, 173
plate trick, 184, 189
Pontrjagin, Lev, 114
product
Cartesian, 40
direct, 40
of matrices, 2
of triangles, 18
product rule, 79
projective line
real, 31
projective plane
octonion, 22
real, 190