Intereting Posts

Exercise books in functional analysis
Do there exist semi-local Noetherian rings with infinite Krull dimension?
$\ell^p\subseteq\ell^q$ for $0<p<q<\infty$ and $\|\cdot\|_p<\|\cdot\|_q$
$1/4$ is in the Cantor set?
A sufficient condition for a domain to be Dedekind?
How do i prove that $\frac{1}{\pi} \arccos(1/3)$ is irrational?
Difference between Gentzen and Hilbert Calculi
An attempt of catching the where-abouts of “ Mysterious group $Ш$ ”
Notation: Why write the differential first?
Value of $\sum_{k=1}^{\infty}\frac{1}{k^2+a^2}$
A question regarding the Power Set Axiom in ZFC
Are there infinite many integer $n\ge 0$ such that $10^{2^n}+1$ prime numbers?
Question(s) about uniform spaces.
Every compact metric space is image of space $2^{\mathbb{N}}$
Basic divisibility fact

I’m looking for a classic matrix algebra reference, either introductory or advanced.

In fact, I’m looking for ways to factorize elements of a matrix, and its appropriate determinant implications.

Your help is greatly appreciated.

- Determine if vectors are linearly independent
- The Eigenvalues of a block matrix
- Why is the permanent of interest for complexity theorists?
- Prove $\ker {T^k} \cap {\mathop{\rm Im}\nolimits} {T^k} = \{ 0\}$
- Prerequisites for Linear Algebra Done Right by Sheldon Axler.
- Solving an equation with LambertW function

- Linear Operators, Representative Matrices and Change of Basis
- Why does this least-squares approach to proving the Sherman–Morrison Formula work?
- Let $B$ be a nilpotent $n\times n$ matrix with complex entries let $A = B-I$ then find $\det(A)$
- Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.
- How to prove that $\sum\limits_{i=0}^p (-1)^{p-i} {p \choose i} i^j$ is $0$ for $j < p$ and $p!$ for $j = p$
- An additive map that is not a linear transformation over $\mathbb{R}$, when $\mathbb{R}$ is considered as a $\mathbb{Q}$-vector space
- Special orthogonal matrices have orthogonal square roots
- If $A$ and $B$ are positive-definite matrices, is $AB$ positive-definite?
- Monotonicity of $\log \det R(d_i, d_j)$
- Clifford Algebra Isomorphic to Exterior Algebra

F. R. Gantmacher’s The Theory of Matrices (2 Volumes)(1959), AMS Chelsea Publishing (trans. K.A. Hirsch), is certainly a classic treatise. I find it useful on occasion for its discussion of Lyapunov stability and eigenvalue/root location via Routh-Hurwitz (vol. 2), but the basics are well-covered in vol. 1.

A bit expensive to buy new, but worth your while keeping an eye out for used copies.

*Golub* and *Van Loan*‘s *Matrix Computations* is kind of a standard reference, but it is actually more oriented towards numerical linear algebra, with a strong emphasize of algorithmic questions, though not without extensive analyses of their theoretical foundations.

Horn and Johnson’s Matrix Analysis is also widely used as a reference. Recently I came across Harville’s Matrix algebra from a statistician’s perspective, and it’s pretty useful too (especially for vec operator and matrix derivatives).

I think Halmos: “Finite Dimensional Vector Spaces” is regarded as a classic by many, though it has a more general approach, i.e. what many people might call “Linear Algebra done right” or something along those lines

.

- Overlapping Probability in Minesweeper
- Searching for a thesis.
- Invertibility of the Product of Two Matrices
- Why are the fundamental groups $\pi_{1}(S^3)$ and $\pi_{1}(S^2)$ trivial?
- Showing the polynomials form a Gröbner basis
- When exactly is the splitting of a prime given by the factorization of a polynomial?
- The logarithm is non-linear! Or isn't it?
- The Plate Trick and $SO(3)$
- Is a box a cylinder?
- Show $\lim\limits_{a \rightarrow + \infty} \int_0^{\infty} \frac{y}{1+y^2}e^{-ay} dy =0 $
- Prove that Pascals triangle contains only natural numbers, using induction.
- Applications of model theory to analysis
- Supremum of measurable function
- Finite Cartesian Product of Countable sets is countable?
- Fibonacci $\equiv -1 \mod p^2$