Intereting Posts

Surely You're Joking, Mr. Feynman! $\int_0^\infty\frac{\sin^2x}{x^2(1+x^2)}\,dx$
Minkowski's inequality
Sum of tangent functions where arguments are in specific arithmetic series
How to prove this summation formula?
Definition of a Cartesian coordinate system
Proving that $X/R$ is Hausdorff $\implies$ $R$ closed.
Given that$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+…+a_1x+a_0$, find $a_7+a_6+a_5+a_4+…+a_1+a_0$
Prove $2^{1092}\equiv 1 \pmod {1093^2}$, and $3^{1092} \not \equiv 1 \pmod {1093^2}$
Examples of functions where $f(ab)=f(a)+f(b)$
Finite number of subgroups $\Rightarrow$ finite group
A question about proving that there is no greatest common divisor
Prove $\sum_{k=0}^{58}\binom{2017+k}{58-k}\binom{2075-k}{k}=\sum_{k=0}^{29}\binom{4091-2k}{58-2k}$
What are the A,B,C parameters of this ellipse formula?
Is it possible to make integers a field?
Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$

Given a set of $n \times n$ real matrices which are linearly independent and commute with one another, how large can the cardinality of this set be? By using diagonal matrices we can have such a set of size $n$ and since diagonal matrices commute with upper triangular ones, we can get $n+1$ too. Can we do better?

What about the case of matrices over finite fields?

- $Tr(A^2)=Tr(A^3)=Tr(A^4)$ then find $Tr(A)$
- How to find the vector equation of a plane given the scalar equation?
- Geometric interpretations of matrix inverses
- Prove two pairs of subspaces are in the same orbit using dimension
- Find minimal set of cosets $C$, so that each $2$ vectors in $A_n$ are in one coset in $C$
- Vandermonde determinant by induction

- $V$ be a vector space , $T:V \to V$ be a linear operator , then is $\ker (T) \cap R(T) \cong R(T)/R(T^2) $?
- How does one prove the matrix inequality $\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge 5^n\det(A^2+B^2+C^2)$?
- Existence of a matrix, characteristic polynomial and minimal polynomial
- Row swap changing sign of determinant
- Stirling Numbers and inverse matrices
- Is a matrix $A$ with an eigenvalue of $0$ invertible?
- The Image of T = Column Space of A
- Verify if symmetric matrices form a subspace
- Rotation by Householder matrices
- Is the matrix $A^*A$ and $AA^*$ hermitian?

Let $n$ be even. Then we can achieve $1+(n/2)^2$ by the matrices of the form

$$\begin{pmatrix} a \cdot \mathrm{Id} & M \\ 0 & a \cdot \mathrm{Id} \end{pmatrix}$$

where each block is $(n/2) \times (n/2)$ and $M$ is arbitrary. This is best possible, by a result of Schur. See “A simple proof of a theorem of Schur”, if you have access to JSTOR.

- How to solve the Riccati's differential equation
- Find $\int \limits_0^\pi \sin(\sin(x))\sin(x)\mathrm dx$
- Proof of Extended Euclidean Algorithm?
- On the centres of the dihedral groups
- “What if” math joke: the derivative of $\ln(x)^e$
- Tensor product of graded algebras
- Find volume of crossed cylinders without calculus.
- Computing the local ring of an affine variety
- Prove that $\sqrt 2 +\sqrt 3$ is irrational.
- $\sqrt x$ is uniformly continuous
- Given a fiber bundle $F\to E\overset{\pi}{\to} B$ such that $F,B$ are compact, is $E$ necessarily compact?
- Prove that every Lebesgue measurable function is equal almost everywhere to a Borel measurable function
- Some basic book to start with modules?
- Partial Differential Equation xp(1+q) = (y+z)q
- $a^2-b^2 = x$ where $a,b,x$ are natural numbers