# Linear Algebra Axler vs Shilov?

1. Nov 9, 2014

### EmSeeSquared

Hi all,

So I'm going to have my first exposure to linear algebra and I've completed Calc 1 and 2.
I've seen Axler and Shilov numerous times and I'm having a hard time choosing it.

Here's my syllabus for my Linear Algebra Course.
Matrices, Gauss reduction, invertibility. Vector spaces, linear independence, spans, bases, row space, column space, null space. Linear maps. Eigenvectors and eigenvalues with applications. Inner product spaces, orthogonality.

For Linear Algebra which one would be best suited for my syllabus? Axler or Shilov. The order in which the content is represented does not matter to me since I'm planning to self learn the whole thing before the classes start in 3-4 months. :)

Now After Linear Algebra, I will have an Introductory Algebra course. The syllabus is below(Please suggest some good books on it as well):

Further linear algebra: equivalence relations, the quotient of a vector space, the homomorphism theorem for vector spaces, direct sums, projections, nilpotent linear transformations, invariant subspaces, change of basis, the minimum polynomial of a linear transformation, unique factorization for polynomials, the primary decomposition theorem, the Cayley-Hamilton theorem, diagonalization. Group theory: subgroups, cosets, Lagrange's theorem, normal subgroups, quotients, homomorphisms of groups, abelian groups, cyclic groups, symmetric groups, dihedral groups, group actions, Caley's Theorem, Sylow's Theorems. Ring theory: rings, subrings, ideals, quotients, homomorphisms of rings, commutative rings with identity, integral domains, the ring of integers modulo n, polynomial rings, Euclidean domains, unique factorization domains. Field theory: subfields, constructions, finite fields, vector spaces over finite fields.

Thanks

2. Nov 10, 2014

### mathwonk

I think Axler is a second book on linear algebra whereas Shilov is an introduction. It will also cover the topics on further linear algebra in your algebra syllabus. That material on group theory and ring theory is in most abstract algebra books. I like Mike Artin's Algebra but there are easier books. My own class notes are free on this page, e.g. the notes for 843-1 are on basic group theory through Sylow.

http://www.math.uga.edu/~roy/

3. Nov 10, 2014

### EmSeeSquared

Thanks :) I'll get Shilov then. And look into your notes. :) Hopefully I'll complete LA and AC during my holidays and next year I can do RA and IA while revising LA and AC :)