Reputation
59,899
Next tag badge:
96/100 score
22/20 answers
Badges
3 50 124
Newest
 Nice Answer
Impact
~925k people reached

1d
revised Minimal polynomial for an invertible matrix and its determinant
added 42 characters in body
1d
answered Minimal polynomial for an invertible matrix and its determinant
1d
comment Minimal polynomial for an invertible matrix and its determinant
This is a weird question, since divisibility over a field is a trivial relation on nonzero elements. If one is asking to show that $\det A=0$ if and only if $b_0=0$, then why not just say so?
1d
revised No minimal polynomial for differentiation operator
spelling
1d
comment Matrix problem, subspace
Obviously this question aims at verifying that you have understood the theory about solving linear systems and row reduction. If for any of the questions it is not clear to you whether the theory gives you that, then you must review your theory. There is no point in us giving you the right answers, as long as you don't understand why.
1d
answered Prove that Z(G) which is the center of G is a subgroup of G
1d
comment The center of a group $G$ is a subgroup of $G$
You should cite the proof precisely. As it stands, there are no assumption made on $a,b$, and the sequence of equalities is therefore largely unjustified (only the first and the last equalities are true without any assumptions). Also the conclusion $ab\in G$ has no relation to the center $Z(G)$.
1d
comment The center of a group $G$ is a subgroup of $G$
@JDrinas but the question was about showing that $Z(G)$ is a subgroup, so one cannot use that fact here.
1d
comment Injective linear mapping maps every plane to a plane through the origin?
The statement is not precise. Planes (without restriction) are not mapped to planes through the origin. After all the identity map is injective and linear, and it does not magically transform planes into planes through the origin. Please correct it, or else it won't be clear what you are asking about precisely.
2d
comment When does reducibility over $\mathbb{Z}_n$ imply reducibility over $\mathbb{Z}$
The first statement is not true without qualification. The polynomial $6X$ is reducible over $\Bbb Z$, but it is irreducible over $\Bbb Z_5$.
2d
comment A Linear Operator of Rank 1
This is just wrong. A Jordan block of size $2$ for $\lambda=0$ is rank one and nilpotent, but not zero.
2d
answered Is every group isomorphic to some nontrivial quotient group?
May
22
comment Little confusion about connectedness
When you say "contrapositive" (which would be an equivalent reformulation, which it is not) you mean "converse" (I'm not sure it really is a converse, but the term converse has no precise definition anyway).
May
22
revised Does matrix has a underlying basis?
added 15 characters in body
May
22
comment Find new generating function, given an arbitrary generating function
@GeoffreyCritzer: Yes, I suppose that is the answer that OP found.
May
22
revised Find new generating function, given an arbitrary generating function
edited body
May
21
comment Find new generating function, given an arbitrary generating function
As for fields of characteristic$~2$, if you don't know what they are then obviously you are not working over one, and just forget the remark. I said so just because you did not say what kind of coefficients your power series have, and in the special case of values in such a field it would not be possible to divide them by$~2$, and my hint would not apply (but again, you need not worry about this eventuality since it is not your case).
May
21
comment Find new generating function, given an arbitrary generating function
@CKKOY: Do you know what even and odd function of (a real value) $x$ are, and that every function of $x$ can be written uniquely as the sum of an even and an odd function? Then projection to the space of even functions is simply mapping $f$ the its even component in this sum (forgetting the odd component). Things are entirely similar for power series, with just a very slight difference in the meaning of "even" and "odd" (for functions "even" means having the same value in any $x$ as in $-x$, for power series it means not changing when $-x$ is substituted for $x$ in the series).
May
21
answered Find new generating function, given an arbitrary generating function
May
20
answered Definition of a geometric sequence