Intereting Posts

Calculate $x$, if $y = a \cdot \sin{}+d$
Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable
Boundedness of solutions for the Laplacian
Albert, Bernard and Cheryl popular question (Please comment on my theory)
Upwind differencing scheme in Finite Volume Method (FVM)
Path components or connected components?
Fractions with radicals in the denominator
Are distinct prime ideals in a ring always coprime? If not, then when are they?
How can I show that $\sup(AB)\geq\sup A\sup B$ for $A,B\subset\mathbb{R}$ where $A\cup B$ is positive and bounded?
Can a proper vector subspace of a Banach space be a countable intersection of dense open subsets?
Cramer's rule: Geometric Interpretation
Elementary proof of a bound on the order of the partition function
Another way of expressing $\sum_{k=0}^{n} \frac{H_{k+1}}{n-k+1}$
Properties of the element $2 \otimes_{R} x – x \otimes_{R} 2$
Proof related to Fibonacci sequence

*I am trying to gather here different meanings of the same symbol, inequality symbol or the succ symbol. I find many other use them so many different ways.*

Sometimes, $A>0$ means $\bar x^T A \bar x >0$. Sometimes, $A>0$ means element-wise i.e. $a_{i,j}>0$ for all $i,j$.

How do I know which definition of inequality people are meaning?

- Similarity of real matrices over $\mathbb{C}$
- Can commuting matrices $X,Y$ always be written as polynomials of some matrix $A$?
- Prove that the rings $End(\mathbb{Z}^{n})$ and $M_{n}(\mathbb{Z})$ are isomorphic
- Can axis/angle notation match all possible orientations of a rotation matrix?
- Trace of a $227\times 227$ matrix over $\mathbb{Z}_{227}$
- A question on commutation of matrices

**Examples**

[Solved]Meaning of this? Why is it $A\succ 0$? LMI and example from Boyd’s book. $\succ$ means positive-definiteness: check PD with Cholenksy decomposition, positive eigen-value check or Sylvester criteria. Chat.Strict matrix inequality defined here requiring symmetric matrices.

- Why is convexity more important than quasi-convexity in optimization?
- How to prove that $\det(M) = (-1)^k \det(A) \det(B)?$
- Differences between a matrix and a tensor
- Proof that Gauss-Jordan elimination works
- Why is this weighted least squares cost function a function of weights?
- Square matrices satisfying certain relations must have dimension divisible by $3$
- Square root of Matrix $A=\begin{bmatrix} 1 &2 \\ 3&4 \end{bmatrix}$
- Matrix with all 1's diagonalizable or not?
- Question about Implicit function theorem
- How do I show that a matrix is injective?

The curved symbol (in my experience) means that the difference is positive definite (so, with zero it means that the matrix is positive definite). The $>$ depends on the context.

For squared matrix $A$, $A>0$ means that $A$ is positive definite. Also, the real parts of all of $A$s eigenvalues are positive.

- Prove a certain property of linear functionals, using the Hahn-Banach-Separation theorems
- Law of large numbers for Brownian Motion (Direct proof using L2-convergence)
- $T(1) = 1 , T(n) = 2T(n/2) + n^3$? Divide and conquer
- What's the difference between simple induction and strong induction?
- Why do we use “congruent to” instead of equal to?
- What is a geometric explanation of complex integration in plain English?
- Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$
- How to show that $\gcd(n! + 1, (n + 1)! + 1) \mid n$?
- Computing $H_1(X)$ using Hurewicz
- Relationship between the cardinality of a group and the cardinality of the collection of subgroups
- Integer solutions of $x^2+5y^2=231^2$
- prove the existence of a measure $\mu$
- Conjectured compositeness tests for $N=k\cdot 2^n \pm 1$ and $N=k\cdot 2^n \pm 3$
- CW complex structure of the projective space $\mathbb{RP}^n$
- Example of a function continuous at only one point.