Intereting Posts

let M be a set of those natural numbers that can be written using only 0's and 1's
Divisibility of prime numbers
How can one find this limit
Suppose p(t)=r(t)s(t) where r(t) is a polynomial with coefficients in the complex numbers. Show r(t) belong to the field of polynomial over R.
Does every Banach space admit a continuous injection to a non-closed subspace of another Banach space?
Show that $n$ lines separate the plane into $\frac{(n^2+n+2)}{2}$ regions
Why do mathematicians use single-letter variables?
If $f \in L^2$, then $f \in L^1$ and$\|f\|_{L^1} \leq \sqrt{2\pi} \|f\|_{L^2}$
Are projection maps open in the Zariski topology?
Which rings containing the complex field are, as vector spaces over that field, isomorphic to $\mathbb{C}^2$?
One sided Chebyshev's inequality
Trigonometric Inequality. $\sin{1}+\sin{2}+\ldots+\sin{n} <2$ .
Comparing complex numbers
How does FFT work?
Is the complement of a countable set in $\mathbb{R}$ dense? Application to convergence of probability distribution functions.

I’m looking for a book to learn Algebra. The programme is the following. The units marked with a $\star$ are the ones I’m most interested in (in the sense I know nothing about) and those with a $\circ$ 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.

$\circ$ **U2:** *Vector Spaces.*

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

- Topology textbook with a solution manual
- What are the applications of functional analysis?
- Reference for Ergodic Theory
- Good book for convergence of series
- Recommend a concise book on mathematical logic
- What are the recommended textbooks for introductory calculus?

$\circ$ **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.**

$\star$ **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.**

$\star$ **U6:** *Linear transformations and matrices.*

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

$\star$ **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 $\mathrm 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 $\mathrm II$which 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?

- What should be the characteristic polynomial for $A^{-1}$ and adj$A$ if the characteristic polynomial of $A$ be given?
- The characteristic and minimal polynomial of a companion matrix
- Advanced Linear Algebra courses in graduate schools
- How to find the multiplicity of eigenvalues?
- What are the possible eigenvalues of a linear transformation $T$ satifying $T = T^2$
- Definiteness of a general partitioned matrix $\mathbf M=\left$
- Prove that $\operatorname{Trace}(A^2) \le 0$
- How to modify a matrix to push all of its eigenvalues into the unit circle?
- Is $B = A^2 + A - 6I$ invertible when $A^2 + 2A = 3I$?
- Understanding dot product of continuous functions

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

Gilbert Strang has a ton of resources on his webpage, most of which are quite good:

Well, I will just add a few online resources that I have used before,

- William Chen’s Lecture Notes
- Jim Hefferon’s Linear Algebra
- Edwin Connell’s Linear Algebra
- Keith Matthew’s Linear Algebra
- Keith Matthew’s Lecture Notes on some advanced linear algebra
- Ruslan Sharipov’s Course of linear algebra and multidimensional geometry

My favorite textbook on the subject **by far** is Friedberg,Insel and Spence’s *Linear Algebra*, 4th edition. It is **very** balanced with many applications,including some not found in most LA books,such as applications to stochastic matrices and the matrix exponetioal function,while still giving a comprehensive and rigorous presentation of the theory.It also has many,many exercises-all of which develop both aspects of the subject further. This is without question my favorite all purpose LA book for the serious mathematics student.

I think I first learned from Charles W. Curtis’ *Linear Algebra: An Introductory Approach*

Please also note that you will want to use “vector” and “morphism” rather than “vectorial” and “morfism” to get the most hits searching in English.

David Lay’s “Linear Algebra and its Applications” is good.

Evar Nering’s book on linear algebra and matrix theory is also an (old but) excellent textbook.

It’s free on archive.org.

- How does “If $P$ then $Q$” have the same meaning as “$Q$ only if $P$ ”?
- Infinite Series $\sum\limits_{n=1}^{\infty}\frac{1}{4^n\cos^2\frac{x}{2^n}}$
- Translation invariant measures on $\mathbb R$.
- Probability that one random number is larger than other random numbers
- Finding $\int e^{2x} \sin{4x} \, dx$
- How to factor the polynomial $5x^2 – 2x – 10$?
- In Lagrange Multiplier, why level curves of $f$ and $g$ are tangent to each other?
- Denseness of the set $\{ m+n\alpha : m\in\mathbb{N},n\in\mathbb{Z}\}$ with $\alpha$ irrational
- Books on topology and geometry of Grassmannians
- Functions that are their Own nth Derivatives for Real $n$
- Understanding construction of open nbds in CW complexes
- Common Problems while showing Uniform Convergence of functions
- Difference between “probability density function” and “probability distribution function”?
- Automation of 3D Paper Modeling
- How do you calculate that $\lim_{n \to \infty} \sum_{k=1}^{n} \frac {n}{n^2+k^2} = \frac{\pi}{4}$?