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I'm currently self-teaching myself Relativity and I'm reading the book Spacetime and Geometry. I came across this expression: expression from the book

What does the $\eta$ represent here? As I understand it the vector $\mathbf x$ is multiplied with the corresponding vector from the dual-space which is $\mathbf x^T$ to get the length squared of the vector. Does the $\eta$ represent a Matrix here? Why is it only applied to the transposed $\mathbf x$? I'm really confused about this and I think I'm just overlooking something, can someobody clarify this?

Jannik Pitt
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1 Answers1

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$\eta$ is the symbol for your metric tensor, usually Minkowski. Basically, this says that the geometry of the space doesn't change in these transformations.

hebetudinous
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