with a weird dot product-like operation called the Minkowski inner product.
Because the Minkowski inner product product is not positive definite, the norm induced by an inner product is a norm, and the space is not a metric space strictly speaking.
The name given to this type of space is a pseudometric space.
This form is not really an inner product in the common modern definition, because it is not positive definite, only a symmetric bilinear form.
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:
but another equivalent one is to use a time positive representation:
The matrix is typically denoted by the Greek letter eta.

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