Intereting Posts

Another way to go about proving the limit of Fibonacci's sequence quotient.
Local coefficients involved in the obstruction class for a lift of a map
Space of bounded continuous functions is complete
Solving Pell's equation(or any other diophantine equation) through modular arithmetic.
Sum of digits of number from 1 to n
Presentations of subgroups of groups given by presentations
Probability distribution of sign changes in Brownian motion
$G/H$ is a finite group so $G\cong\mathbb Z$
Quick way of finding the eigenvalues and eigenvectors of the matrix $A=\operatorname{tridiag}_n(-1,\alpha,-1)$
Why not write the solutions of a cubic this way?
Tossing a coin with at least $k$ consecutive heads
The smallest symmetric group $S_m$ into which a given dihedral group $D_{2n}$ embeds
finite fields, a cubic extension on finite fields.
“Negative” versus “Minus”
Brownian Motion Conditional Expectation Question

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
- Math and Music theory books
- Introductory text for calculus of variations
- Very good linear algebra book.
- Intermediate Text in Combinatorics?
- What is the best calculus book for my case?

$\circ$ **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 is the difference between matrix theory and linear algebra?
- Square root of Positive Definite Matrix
- Why is an orthogonal matrix called orthogonal?
- Is a field determined by its family of general linear groups?
- invertible if and only if bijective
- How to prove the Pythagoras theorem using vectors
- A lower bound for the ratio of $2$- and $\infty$-norms within a linear subspace
- Union of conjugacy classes of $O(n)$ is not a subgroup
- Finding number of matrices whose square is the identity matrix
- New proof about normal matrix is diagonalizable.

“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.

- Growth of $\Gamma(n+1,n)$ and $\operatorname{E}_{-n}(n)$
- How to prove that if each element of group is inverse to itself then group commutative?
- Fill in the hole for the proof for $f^*(w \wedge \theta) = (f^*w) \wedge (f^* \theta)$
- How to calculate the gradient of log det matrix inverse?
- Flatness and intersection of ideals
- Where does the “Visual Multiplication” technique originate from?
- Triangle and Incircle
- Uniform convergence and integration
- If $\gcd(a,b)=1$, is $\gcd(a^x-b^x,a^y-b^y)=a^{\gcd(x,y)}-b^{\gcd(x,y)}$?
- What does it mean to differentiate in calculus?
- Log concavity of binomial coefficients: $ \binom{n}{k}^2 \geq \binom{n}{k-1}\binom{n}{k+1} $
- Taylor series for $\sqrt{x}$?
- Complex Analysis Question from Stein
- Method of characteristics for a system of pdes
- Why maximal atlas