OurBigBook
About
$
Donate
Sign in
Sign up
The orthogonal group is the group of all matrices that preserve the dot product
ID: the-orthogonal-group-is-the-group-of-all-matrices-that-preserve-the-dot-product
Top articles
Latest articles
New article in topic
Show body
Body
0
The orthogonal group is the group of all matrices that preserve the dot product
by
Ciro Santilli
37
Updated
2025-07-16
When viewed
as
matrices
, it is the
group
of all
matrices
that preserve the
dot product
,
i
.e.:
O
(
n
)
=
O
∈
M
(
n
)
∣∀
x
,
y
,
x
T
y
=
(
O
x
)
T
(
O
y
)
(1)
This implies that it also preserves important geometric notions such
as
norm
(intuitively:
distance
between two points) and
angles
.
This is perhaps the best "default
definition
".
Total
articles
:
1
New to
topics
?
Read the docs here!
