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Implicit metric signature in Einstein notation
Ciro Santilli
(
@cirosantilli,
37
)
...
Mathematics
Area of mathematics
Algebra
Linear algebra
Tensor
Einstein notation
Updated
2025-07-16
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Then
a
specific
metric
is involved, sometimes
we
want to automatically add it to products.
E.
g
., in
a
context
considering the common
Minkowski inner product matrix
where the
η
4x4
matrix
and
μ
is
a
vector in
R
4
x
μ
x
μ
=
x
μ
η
μν
x
ν
=
−
x
0
2
+
x
1
2
+
x
2
2
+
x
3
2
;
(1)
which
leads
to the change of
sign
of some terms.
Ancestors
(7)
Einstein notation
Tensor
Linear algebra
Algebra
Area of mathematics
Mathematics
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