std::linalg is based on the dense BLAS as specified in Chapter 2 of the BLAS Technical Forum Standard ( https://www.netlib.org/blas/blast-forum/chapter2.pdf ), and focuses on the subset of routines that appear in the "Reference BLAS" with its core of BLAS 1, 2, and 3 routines (source: Section 9.1 of the std::linalg main proposal P1673: https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2023/p1673r13.html ). Vector cross products are not in the BLAS Standard.

Sections 6 - 10 of P1673 clarify std::linalg's design. Section 9 in particular explains "What we exclude from the design" and why.

FYI, the version of P1673 that was voted into the C++ Working Draft was R13.