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by
Ciro Santilli
(@cirosantilli,
32
)
Lie algebra of
G
L
(
n
)
tags:
Lie algebra of a matrix Lie group
Is the
set of all n-by-y square matrices
.
Because
G
L
(
n
)
is a
Lie group
we can use
Section "Lie algebra of a matrix Lie group"
.
For every matrix
x
in the
set of all n-by-y square matrices
M
n
,
e
x
has inverse
e
−
x
.
Note that this works even if
x
is not
invertible
, and therefore not in
G
L
(
n
)
!
Therefore, the Lie algebra of
G
L
(
n
)
is the entire
M
n
.
Ancestors
Important Lie group
Lie group
Differential geometry
Geometry
Area of mathematics
Mathematics
Index
Incoming links
Lie algebra of a matrix Lie group
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