For Galois theory, took an oral exam on what was in Herstein.
For linear algebra where the field is any of the rationals, reals, complex, and finite fields there is
Evar D.\ Nering,
{\it Linear Algebra and Matrix Theory,\/}
John Wiley and Sons,
New York,
1964.\ \
As I recall, Nering was an Artin student at Princeton.
Some of the proofs for the rational, real, or complex fields don't work for finite fields so for those need special proofs.
Had a course in error correcting codes -- it was applied linear algebra where the fields were finite.
Linear algebra is usually about finite dimensional vector spaces with an inner product (some engineers say dot product), but the main ideas generalize to infinite dimensions and Hilbert and Banach spaces.
I.\ N.\ Herstein, {\it Topics in Algebra,\/}
(markup for TeX word processing).
For Galois theory, took an oral exam on what was in Herstein.
For linear algebra where the field is any of the rationals, reals, complex, and finite fields there is
Evar D.\ Nering, {\it Linear Algebra and Matrix Theory,\/} John Wiley and Sons, New York, 1964.\ \
As I recall, Nering was an Artin student at Princeton.
Some of the proofs for the rational, real, or complex fields don't work for finite fields so for those need special proofs.
Had a course in error correcting codes -- it was applied linear algebra where the fields were finite.
Linear algebra is usually about finite dimensional vector spaces with an inner product (some engineers say dot product), but the main ideas generalize to infinite dimensions and Hilbert and Banach spaces.