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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
(9)
Symmetric bilinear form
Symmetric bilinear map
Multilinear map
Linear map
Linear algebra
Algebra
Area of mathematics
Mathematics
Home
Incoming links
(3)
Dot product
Symmetric matrix
What happens to the definition of the orthogonal group if we choose other types of symmetric bilinear forms
Synonyms
(1)
Matrix representation of the symmetric bilinear form
Ciro Santilli
OurBigBook.com