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by Ram_1729
Sun Mar 31, 2019 7:43 pm
Forum: Real Analysis
Topic: Nowhere dense of linear subspace of at most n-1
Replies: 0
Views: 307

Nowhere dense of linear subspace of at most n-1

Let $W\subset \mathbb{R}^n$ be a linear subspace of dimension at most $n-1$. Which of the following statements are true ??
a)$W$ is nowhere dense
b)$W$ is closed
c)$\mathbb{R}^n-W$ is connected
d)$\mathbb{R}^n-W$ is not connected
by Ram_1729
Wed Dec 05, 2018 10:41 pm
Forum: General Topology
Topic: $\mathbb{R}^2 \setminus \mathbb{Q} \times \mathbb{Q}$
Replies: 2
Views: 1370

Re: $\mathbb{R}^2 \setminus \mathbb{Q} \times \mathbb{Q}$

No take a sequence $(2+\frac{\sqrt{2}}{n},\sqrt{2})\to (2,\sqrt{2})$
by Ram_1729
Wed Dec 05, 2018 10:27 pm
Forum: Algebraic Structures
Topic: Find the number of homomorphism
Replies: 1
Views: 397

Find the number of homomorphism

How to find the number of homomorphism of these
a)$$Q_8\to K_4$$
b)$$K_4\to S_n(n\neq 4)$$
c)$$K_4\to S_4$$
by Ram_1729
Mon Dec 03, 2018 5:44 pm
Forum: Linear Algebra
Topic: Eigenvalues of Symmetric Matrices
Replies: 1
Views: 440

Eigenvalues of Symmetric Matrices

For any two symmetric $n\times n$ matrices $A$ and $B$ be their eigenvalues be ordered from largest to smallest . How to prove that for eigenvalues $|\lambda _k^A-\lambda _k^B|\le ||A-B||$ for $1\le k\le n$. Where $\lambda _k^A,\lambda _k^B$ are respective eigenvalues of $A$ and $B$