Intereting Posts

Is inverse matrix convex?
Exponential of a polynomial of the differential operator
Markov processes driven by the noise
Partial summation of a harmonic prime square series (Prime zeta functions)
Determinant of circulant matrix
To show for following sequence $\lim_{n \to \infty} a_n = 0$ where $a_n$ = $1.3.5 … (2n-1)\over 2.4.6…(2n)$
Show that $ \sqrt{(z-1)(z-2)(z-3)} $ can be defined on the entire plane minus .
A question about orientation on a Manifold
Proof by induction that $n!\gt 2^{n}$ for $n \geq 4$
Power of commutator formula
Proving that $\pi(2x) < 2 \pi(x) $
Using a compass and straightedge, what is the shortest way to divide a line segment into $n$ equal parts?
Evaluating $\int_{-3}^{3}\frac{x^8}{1+e^{2x}}dx$
Show that if $f(z)$ is a continuous function on a domain $D$ such that $f(z)^N$ is analytic for some integer $N$, then $f(z)$ is analytic on $D$.
Is $\ 7!=5040\ $ the largest highly composite factorial?

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.

- How to divide polynomial matrices
- Is a bra the adjoint of a ket?
- What can be computed by axiomatic summation?
- Non-numerical vector space examples
- For $T\in \mathcal L(V)$, we have $\text{adj}(T)T=(\det T)I$.
- Existence of Hamel basis, choice and regularity

- Eigenvector of matrix of equal numbers
- An equivalent condition for a real matrix to be skew-symmetric
- There exists $C\neq0$ with $CA=BC$ iff $A$ and $B$ have a common eigenvalue
- Composition of linear maps
- Geometric interpretation of matrices
- When is a symmetric 2-tensor field globally diagonalizable?
- Another proof of uniqueness of identity element of addition of vector space
- Invariant subspaces using matrix of linear operator
- Matrix to power $2012$
- Angle between two vectors?

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

.

- Easy visualizations of small countable ordinals
- Limit of measures is again a measure
- Prove that free modules are projective
- Physical Meaning of Minkowski Distance when p > 2
- How can I evaluate $\int_{-\infty}^{\infty}\frac{e^{-x^2}(2x^2-1)}{1+x^2}dx$?
- Proving the pairing axiom from the rest of ZF
- Help finding the fundamental group of $S^2 \cup \{xyz=0\}$
- Plotting a Function of a Complex Variable
- Traffic flow modelling – How to identify fans/shocks?
- Caratheodory: Measurability
- If $u$ is harmonic and bounded in $0 < |z| < \rho$, show that the origin is a removable singularity
- Derivative of $x^x$
- Computing an integral basis of an algebraic function field, $y^4-2zy^2+z^2-z^4-z^3=0$.
- Is there any formula for the series $1 + \frac12 + \frac13 + \cdots + \frac 1 n = ?$
- Sum of stars and bars