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Minkowski inner product matrix (
η
μ
ν
)
Minkowski inner product
nosplit
words:
121
The
matrix representation of the symmetric bilinear form
that is the
Minkowski inner product
.
Since that is a
symmetric bilinear form
, the associated
matrix
is a
symmetric matrix
.
By default, we will use the time negative representation unless stated otherwise:
η
μ
ν
=
⎣
⎢
⎢
⎢
⎡
−
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
⎦
⎥
⎥
⎥
⎤
(9)
but another equivalent one is to use a time positive representation:
η
μ
ν
=
⎣
⎢
⎢
⎢
⎡
1
0
0
0
0
−
1
0
0
0
0
−
1
0
0
0
0
−
1
⎦
⎥
⎥
⎥
⎤
(10)
The matrix is typically denoted by the
Greek letter eta
.
Ancestors
Minkowski inner product
Minkowski space
Spacetime
Special relativity
Relativity
Particle physics
Physics
Natural science
Science
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Implicit metric signature in Einstein notation