What is a good book to study linear algebra?

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 Algebra by Armando Rojo and have Linear Algebra by 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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