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by Ciro Santilli (@cirosantilli, 37)

Minkowski inner product matrix (ημν​)

 ... Particle physics Relativity Special relativity Spacetime Minkowski space Minkowski inner product
 0 By others on same topic  0 Discussions  Updated 2025-05-23  +Created 1970-01-01  See my version
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:
ημν​=​−1000​0100​0010​0001​​
(1)
but another equivalent one is to use a time positive representation:
ημν​=​1000​0−100​00−10​000−1​​
(2)
The matrix is typically denoted by the Greek letter eta.

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  • Implicit metric signature in Einstein notation

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