I’m looking for a book to learn Algebra. The programme is the following. The units marked with a ⋆ are the ones I’m most interested in (in the sense I know nothing about) and those with a ∘ are those which I’m mildly comfortable with. The ones that aren’t marked shouldn’t be of importance. Any important topic inside a unite will be boldfaced.

U1:Vector Algebra.

Points in the n-dimensional space. Vectors. Scalar product. Norm. Lines and planes. Vectorial product.∘

U2:Vector Spaces.

Definition. Subspaces. Linear independence. Linear combination. Generating systems. Basis. Dimesion. Sum and intersection of subspaces. Direct sum. Spaces with inner products.∘

U3:Matrices and determinants.

Matrix Spaces. Sum and product of matrices. Linear ecuations. Gauss-Jordan elimination. Range.Roché Frobenius Theorem. Determinants. Properties. Determinant of a product. Determinants and inverses.⋆

U4:Linear transformations.

Definition. Nucleus and image. Monomorphisms, epimorphisms and isomorphisms. Composition of linear transformations. Inverse linear tranforms.

U5:Complex numbers and polynomials.

Complex numbers. Operations. Binomial and trigonometric form. De Möivre’s Theorem.

Solving equations. Polynomials. Degree. Operations. Roots. Remainder theorem. Factorial decomposition. FTA.Lagrange interpolation.⋆

U6:Linear transformations and matrices.

Matrix of a linear transformation. Matrix of the composition. Matrix of the inverse. Base changes.⋆

U7:Eigen values and eigen vectors

Eigen values and eigen vectors. Characteristc polynomial. Aplications. Invariant subspaces. Diagonalization.To let you know, I own a copy of Apostol’s Calculus I which has some of those topics, precisely:

- Linear Spaces
- Linear Transformations and Matrices.
I also have a copy of Apostol’s second book of Calc IIwhich continues with

- Determinants
- Eigenvalues and eigenvectors
- Eigenvalues of operators in Euclidean spaces.
I was reccommended

Linear Algebraby Armando Rojo and haveLinear Algebraby Carlos Ivorra, which seems quite a good text.What do you reccomend?

**Answer**

“Linear Algebra Done Right” by Sheldon Axler is an excellent book.

**Attribution***Source : Link , Question Author : Community , Answer Author :
Amihai Zivan
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