Ciro Santilli
OurBigBook.com
$£ Sponsor €¥
中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件 邓家贵、低端人口、西藏骚乱
Matrix representation of a symmetric bilinear form
...
Algebra
Linear algebra
Linear map
Multilinear map
Symmetric bilinear map
Symmetric bilinear form
OurBigBook.com
words: 71
Like the
matrix representation of a bilinear form
, it is a
matrix
, but now the matrix has to be a
symmetric matrix
.
We can then immediately see that the matrix is symmetric, then so is the form. We have:
B
(
x
,
y
)
=
x
T
M
y
(20)
But because
B
(
x
,
y
)
is a
scalar
, we have:
B
(
x
,
y
)
=
B
(
x
,
y
)
T
(21)
and:
B
(
x
,
y
)
=
B
(
x
,
y
)
T
=
(
x
T
M
y
)
T
=
y
T
M
T
x
=
y
T
M
T
x
=
y
T
M
x
=
B
(
y
,
x
)
(22)
Ancestors
Symmetric bilinear form
Symmetric bilinear map
Multilinear map
Linear map
Linear algebra
Algebra
Area of mathematics
Mathematics
Ciro Santilli's Homepage
Incoming links
Dot product
Symmetric matrix
What happens to the definition of the orthogonal group if we choose other types of symmetric bilinear forms
Synonyms
Matrix representation of the symmetric bilinear form