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Row-major

Matrix multiplication

$$C=AB$$

$$C^T=(AB)^T=B^T A^T$$

possible

Solve/LU factorization

Hermitian factorization

$$A=LDL^T$$ $$A^T=(LDL)^T=L^T D^T L$$

possible

Inversion

same as solve

Least squares

will require a transpose

QR

will require a transpose

Cholesky

$$A=LL^T$$ $$A^T=L^TL$$

possible

SVD

$$A=UDV^T$$ $$A^T=(UDV^T)^T = VD^TU^T$$

possible

determinant

just uses the diagonals of decompositions, representation irrelevant