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absolute0
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5 votes
Accepted

Show that if $X^*AX\in \mathbb{R}$, then $A$ is hermitian

3 votes

Application of Hahn–Banach theorem

3 votes

Calculus - Sequence and Function - hard exercise

3 votes
Accepted

Functional equation - unique solution

2 votes
Accepted

Prove that the following linear transformation is surjective

2 votes
Accepted

Do Linear Transformations exist over vector spaces whose addition rules are not ordinary?

2 votes
Accepted

Is the null space of a matrix the same after you multiply it by more matrices?

2 votes

Norm - Cauchy Sequence

2 votes

Question about the proof for "The rational line Q does not have the completeness property"

2 votes
Accepted

If $A - B \succ 0$, is $AB^{-1} -I \succeq 0$?

1 vote

Is a pseudometric $d(\cdot,x)$ continuous for fixed $x$?

1 vote
Accepted

Showing that if $f$ and $g$ are continuous at $a$ then $c_1f + c_2g$ is also continuous at $a$

1 vote

$S_1, S_2,...,S_k$ are subsets of $V$ such that, prove that $V = \operatorname{span}\{S_1\} + \dotsb + \operatorname{span}\{S_k\}$.

1 vote

If f is continuous on [a,b] and f(a)=f(b) then show that there exists x,y in (a,b) such that f(x)=f(y)

1 vote

Does $[0,+ \infty)$ counts for a closed interval in extended real number system?

1 vote

Convergence of $\sum \frac{\sqrt{a_n}}{n^r}$, given $\sum a_n$.

1 vote

Contraction Mapping and fixed point

1 vote
Accepted

If $\lim_{x\to a} |g(x)| =\lim_{x\to a} |\frac{f(x)}{g(x)}| = \infty$, is it true that $\lim_{x\to a} f(x) + g(x) = \lim_{x\to a} f(x)$?

1 vote
Accepted

How to prove that the following statements are equivalent: $\lim_{n\to \infty} a_n = a$ and $\lim_{x\to 0} \bar{\alpha}(x) = a$

1 vote

If $\lim_{x \to 0}g(x)=L$. How do I prove $\lim_{h \to 0} g(f(x+h)-f(x)) = \lim_{y \to 0}g(y)$ using $\epsilon-\delta$

1 vote

limit of the indicator function

1 vote
Accepted

Uniform convergence of $(f_n)_{n \in \Bbb{N}}$ on $D_1 \cup D_2$

1 vote

The sum of subspaces of $V$ is the smallest subspace of $V$ containing each of the subspaces

1 vote
Accepted

Proving $\lim_{x\to0}\frac{e^{1/x}-1}{e^{1/x}+1}$ does not exist, using epsilon-delta

1 vote
Accepted

Let X be a Compact metric space and $F\subset C(X)$ be a compact subset. Show that F is equicontinuous.

1 vote

Simple Compactness and Continuity Proof Verification

1 vote
Accepted

Cauchy sequences proof

1 vote

Alternating series - determine if it converges absolutely, conditionally or diverges using alternating p-series test

1 vote
Accepted

Surjections, Bijections, and Injections

1 vote

Prove that the closure of a connected subset is also connected