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16h
awarded  Nice Question
22h
comment Why do we have “another” definition for the kernel?
Let $f:X\to Y$ such that $Y$ has identity called $y$, then $\ker(f)=f^{-1}(y)$.
22h
asked Why do we have “another” definition for the kernel?
1d
comment Computing $\operatorname{Tr} \bigl( \bigl( (A+I )^{-1} \bigr)^2\bigr)$
@Boby, you should convince yourself (google or prove it yourself) that adding the identity to a matrix will shift the eigenspectrum in the manner of this proof (on line one).
1d
comment Computing $\operatorname{Tr} \bigl( \bigl( (A+I )^{-1} \bigr)^2\bigr)$
Could be helpful: math.stackexchange.com/questions/391128/…
1d
revised Is the identity map a diffeomorphism?
added 20 characters in body
Jul
27
awarded  Popular Question
Jul
23
comment Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?
Old post, but.... I think the fact that the limit of a ratio is not a ratio (the derivative) is sooo much like the fact the limit of a rational sequence need not be rational. In fact, the analogy is perfect, but instead of rational numbers it's the limit of rational functions.
Jul
22
comment How to Tell If Matrices Are Linearly Independent
Equivalently, if there are $\alpha$ and $\beta$ such that at least one of them is nonzero, then if $A$ and $B$ are nonzero this forces the other coefficient to be nonzero. So solving, we get $\gamma A = B$ where $\gamma = -\alpha / \beta$. In other words, two non-zero matrices are linearly dependent if and only if one is a multiple of the other.
Jul
19
comment linear map $f:V \rightarrow V$, which is injective but not surjective
I thought it worth mentioning this is the right shift operator.
Jul
10
comment Finding $C$ such that $\frac{1}{\sqrt{x} - \sqrt{a}} < C $ where $a\geq 0$
If $x$ is a variable and $a$ is a constant then this is not possible. Simply let $x\to 0$ then $\frac{1}{\sqrt{x}-\sqrt{a}}\to \infty$
Jul
10
comment Diagonalization of non-orthogonal projection
But are the diagonalized by unitary matrices?
Jun
23
awarded  Necromancer
Jun
10
comment Continuity of a function $f: \mathbb{R}^2 \to \mathbb{R}$
Is this the integral of a function? If so then it is obviously continuous by the FTC
Jun
8
revised Notation from Bowen's Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms
added 12 characters in body
Jun
3
revised Why study Bergman Spaces?
edited tags
Jun
3
comment Why study Bergman Spaces?
Seems like Leo Sera (who edited this post) added the tag, I don't see many things on bergman spaces... however that may change in time. I'd just leave it as is and I'll take down another tag.
May
29
accepted “Least upper bound property for a poset is equivalent to greatest lower bound property” vs existence of sup given inf
May
29
comment “Least upper bound property for a poset is equivalent to greatest lower bound property” vs existence of sup given inf
Yes, $(A,\le)$ is my poset. Because the inf always exists then $\inf(\emptyset)\in A$, and if there were another element, say $x$, greater than all elements of $A$ the above argument would also show that it's less than or equal to $\inf(\emptyset)$ hence equal to $\inf(\emptyset)$. I guess working with the empty set is a little weird, I'm actually surprised there was nothing wrong with the homework.
May
29
comment “Least upper bound property for a poset is equivalent to greatest lower bound property” vs existence of sup given inf
Yes, but I was a little confused by it. I'm assuming that if the set of least upper bounds for a subset $S$ is empty then inf($\emptyset)=\sup(A)$ and this is an upper bound for $S$, contradicting that the set of upper bounds is empty. It just doesn't quite feel right, I realize $\emptyset\subset A$ and so $\inf(\emptyset)$ exists by our assumption, but I suppose I don't see why $\sup(A)$ exists, if it exists then I believe they are equal.