New posts in linear-algebra

Why in the proof of $A\cdot Adj(A)=Det(A)\cdot I_n$ entires not on the diagonal are zero?

Chameleons of Three Colors puzzle

linear-algebra modular-arithmetic puzzle proof-explanation

Integrate $ \int_0^\infty \left( ( x A+I)^{-1} A - \frac{1}{c+x} I \right)\, \mathrm dx $ where $A$ is positive-definite and $c>0$

linear-algebra integration multivariable-calculus

Eigenvalues of inverse matrix to a given matrix

linear-algebra matrices eigenvalues-eigenvectors

$\operatorname{rank}(A^2)+\operatorname{rank}(B^2)\geq2\operatorname{rank}(AB)$ whenever $AB=BA$?

linear-algebra matrices inequality matrix-rank

Did I just discover a new way to calculate the signature of a matrix?

linear-algebra matrices algebra-precalculus symmetric-matrices matrix-congruences

Must any nth order homogeneous ODE have n solutions?

linear-algebra ordinary-differential-equations fundamental-solution

Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric

linear-algebra matrices

Heronian triangle Generator

linear-algebra geometry algorithms diophantine-equations triangles

Finding Euler decomposition of a symplectic matrix

linear-algebra matrices matrix-decomposition svd symplectic-linear-algebra

If the sum of eigenvectors is an eigenvector, then they all correspond to the same eigenvalue

linear-algebra proof-verification proof-writing eigenvalues-eigenvectors

Angle between two planes in four dimensions

Dimension of $GL(n, \mathbb{R})$

linear-algebra matrices

How to take the derivative of a matrix with respect to itself?

linear-algebra derivatives matrix-calculus

Decompose invertible matrix $A$ as $A = LPU$. (Artin, Chapter 2, Exercise M.11)

linear-algebra matrices numerical-linear-algebra gaussian-elimination lu-decomposition

How is $\mathrm{PGL}(V)$ a subgroup of $\mathrm{P\Gamma L}(V)$?

linear-algebra abstract-algebra group-theory permutations linear-groups

Understanding determinant $=0$

linear-algebra matrices vector-spaces determinant

Proving that L(V) cannot be finite dimensional given an identity.

linear-algebra linear-transformations

Kantorovich inequality and Cauchy-Schwarz inequality

linear-algebra inequality eigenvalues-eigenvectors cauchy-schwarz-inequality

General Steinitz exchange lemma

linear-algebra abstract-algebra reference-request vector-spaces