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May
23
revised Vectors in an inner product space
Please use `\langle \rangle` and `\|` instead of `<>` and `||`.
May
23
revised linear algebra-norm of matrix
deleted 1 character in body
May
23
revised Is $\ker(nat_{H})=H$ a true statement?
edited title
May
23
revised Why is the identity map from $S^1$ to $S^1$ not homotpic to the constant map?
edited tags
May
23
revised How to use Itō in this very simple case
ô is not used in the romanization of Japanese. It should be ō and it means long-o.
May
22
revised Is $\coprod \subseteq \prod$ true in any (complete cocomplete) Abelian category?
edited body
May
21
comment A Hausdorff, Baire space must be σ -compact?
If $X$ is Hausdorff Baire $\sigma$-compact space then it is countable union of compact sets, and at least such compact set has nonempty interior.
May
21
answered Show if it is lipschitz continuous?
May
18
revised When will $\operatorname{det}\left(A\cdot A^{\top}\right)=0$?
added 228 characters in body
May
18
comment When will $\operatorname{det}\left(A\cdot A^{\top}\right)=0$?
@baharampuri Yes, you are right. I forgot that $\operatorname{rank}AA^T = \operatorname{rank} A$ holds only for the real matrices. (See Leon's "Linear algebra with applications" exercise 5.2.13) If you use the conjugate transpose instead of ordinary transpose, you get $\operatorname{rank} AA^* = 1$.
May
18
answered When will $\operatorname{det}\left(A\cdot A^{\top}\right)=0$?
May
18
comment When will $\operatorname{det}\left(A\cdot A^{\top}\right)=0$?
For square matrix $A$, $\det AA^T = 0$ if $A$ is singular. Conversely, $\det AA^T $ is not zero if $A$ has invertible matrix.
May
16
answered Prove that $f(z)$ is of the $Ce^{z}$
May
16
comment Prove that $f(z)$ is of the $Ce^{z}$
What is $x$? $\!\,$
May
16
revised Prove that $f(z)$ is of the $Ce^{z}$
added 15 characters in body
May
16
revised how mental math is helpful to learn math? is it any scope for research or to improve new vedic math tricks?
edited tags
May
16
comment Proving that $n|x^ {φ(n)/2} − 1$ for every $x$ coprime to $n$.
@Meitar $\phi(n)$ is even if $n>2$. Recall the formula $\phi(n) = n\prod_{p\mid n} \left(1-\frac{1}{p}\right)$.
May
16
comment How Many Countable Models of the successor function
Every model of the theory $T_S$ is isomorphic to the union of set of natural numbers and copies of set of integers (with usual ordering).
May
16
accepted Is there a name of the dual of quotient?
May
16
comment Is there a name of the dual of quotient?
Thanks for your answer, but it is not an answer I want. We do not call $G/H$ a cokernel ordinarily (I don't certain it since I don't know well about category theory and related fields.) My question I intended is, there is known notations of $A;B$ in my question used widely. (I am sorry if you misunderstand my question because of the ambiguity of my asking.)