- #1

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- TL;DR Summary
- Is this adequate?

I'm writing some notes for myself (to read in my rapidly approaching declining years) and I'm wondering if this statement is correct. I"m not sure I am posting this question in the right place.

"Summary: The matrix representations of isometric (distance-preserving) subgroups of the general linear group GL(V), acting on the n-dimensional vector space V, are the orthogonal or unitary matrices, and the Lorentz transformations – O(n), U(n) and O(1,3). The parameter n is the dimension of the vector space and of the group. Both O(n) and U(n) have subgroups characterized as “special”, meaning that they contain only those matrices whose determinant is +1."

I'm especially unsure about that "acting on". Thanks in advance for considering something so simple.

"Summary: The matrix representations of isometric (distance-preserving) subgroups of the general linear group GL(V), acting on the n-dimensional vector space V, are the orthogonal or unitary matrices, and the Lorentz transformations – O(n), U(n) and O(1,3). The parameter n is the dimension of the vector space and of the group. Both O(n) and U(n) have subgroups characterized as “special”, meaning that they contain only those matrices whose determinant is +1."

I'm especially unsure about that "acting on". Thanks in advance for considering something so simple.