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Sep
30
awarded  Explainer
Sep
6
comment Can there exist a non diagonal matrix whose inverse is diagonal matrix?
Yes, it is like in a field with respect to addition or multiplication or like in a vector space with respect to addition.
Sep
2
answered Kernel of linear transformation composition
Sep
2
comment Can there exist a non diagonal matrix whose inverse is diagonal matrix?
The inverse matrix of a diagonal matrix $\mathrm{diag}(\lambda_1, \ldots, \lambda_n)$ is the diagonal matrix $\mathrm{diag}(\frac{1}{\lambda_1}, \ldots, \frac{1}{\lambda_n})$ and the inverse is unique so no.
Sep
1
answered If $\mathcal{B}^*$ is a basis for $V^*$, then $V^*$ is finite dimensional.
Sep
1
revised Integration against divergence free vector fields
added 401 characters in body
Sep
1
answered Integration against divergence free vector fields
Aug
30
comment Integration against divergence free vector fields
Is this true when $n = 1$?
Aug
30
revised proof that a continuous additive homomorphism $\mathbb{R}^n\to\mathbb{R}^m$ is $\mathbb{R}$-linear
added a hypothesis that appears in the title but not in the question itself
Jul
29
answered What's going on here with zero divisors and invertibility?
Jul
21
answered diagonalization of a matrix over finite fields
Jul
21
answered Proof that this set is not compact
Jul
21
answered Eigenspace, Diagonalizable, Direct Sum
Jul
21
revised Eigenspace, Diagonalizable, Direct Sum
Formatting
Jul
18
revised alternating series test convergence proof with Cauchy criterion
Formatting, grammar
Jul
17
comment homeomorphism non-example
I only argued that $\varphi$ is not a homeomorphism, not that other homeomorphisms aren't possible. This is also true - a topological space $X$ is called sequentially compact if every sequence $(x_n)$ of points in $X$ has a convergent subsequence. This is a topological notion and so preserved by homeomorphisms - if a space is sequentially compact then any space homeomorphic to it is also sequentially compact. The circle $S^1$ is sequentially compact while both $[0,1)$ and $\mathbb{R}$ aren't. Finally, like you wrote, locally, $\mathbb{R}$ and $S^1$ are homeomorphic.
Jul
17
reviewed Approve suggested edit on sum of the series $\sum_{k=0}^{\infty}(k+1)(1-|x_k|)|x_n|^k$
Jul
17
reviewed Reject suggested edit on $f:X\rightarrow S^1$ a continuous map. $X$ a path-connected topological space.
Jul
17
reviewed Approve suggested edit on Characterize graph by its connectivity matrix
Jul
17
revised homeomorphism non-example
added 368 characters in body