Starred posts | chat.stackexchange.com

PM 2Ring

Jun 15 09:40

Some rooms use Oakbot. But IMHO that cure is worse than the disease. ;) stackoverflow.com/users/4258326/oakbot

PM 2Ring

Jun 14 01:52

@MartinSleziak There's a reliable bot named Toasty that stops rooms from getting frozen. stackapps.com/q/10422 It's very easy for a room owner to set up.

Jakobian

Apr 20 01:28

@Færd I want to note this fails for continuous operators between Banach spaces, which your book might be interested in given it's about physics. Namely, the operator $T:\ell^1\to \ell^2$ given by $T(x) = x$ is an example where $T^\ast$ fails to be surjective.

Færd

Apr 19 16:51

This is from Sadri Hassani's Mathematical Physics. In Proposition 2.5.5, I get why "If T is surjective, then T∗ is injective", but I don't get why "If T is injective, then T∗ is surjective". Could anyone help me with that?

Antony Theo.

Jan 27 16:38

Hello! I am studying for an exam and had a question.

Let E be a subspace defined by the span of a set of vectors and F be the orthogonal complement of E. Is the null space of the projection matrix onto E the basis of F?

Martin Sleziak

Jan 3 05:52

@ydd There is a related post on the main site: Is there a name for a square matrix with constant diagonal and off-diagonal elements?

rschwieb

Jan 23, 2023 15:49

I had thought there was a commutative algebra room out there, but I couldn't spot it. Here is a commutative algebra request I dropped in the mathematics chat but I suspect it will get buried quickly: chat.stackexchange.com/transcript/message/62828054#62828054

Tapi

Nov 1, 2022 18:42

Let M be an n × m real matrix. Consider the following:
• Let k1 be the smallest number such that M can be factorized as A · B, where A
is an n × k1 and B is a k1 × m matrix.
• Let k2 be the smallest number such that $M =\sum_{i=1}^{k_2} u_i*v_i$, where each $u_i$ is an n × 1 matrix and each $v_i$ is an 1 × m matrix.
• Let k3 be the column-rank of M.
Can someone help me with proving k1 = k2 = k3?

BAYMAX

Aug 26, 2022 06:13

I am trying to understand the continuity argument used in the second answer..any help is much appreciated?
I am trying to understand why there cannot be a continuous path to the region $D_{a}<0$ and $D_{b}<0$ ?

BAYMAX

Aug 13, 2022 06:12

I am struggling to understand eqn (2) and (3)

BAYMAX

Aug 13, 2022 06:11

6

Q: Is it impossible for determinants of these matrices to both be negative?

Suppose $A,B \in M_{n}(\Bbb{R})$ such that $A = \left[C_{1}\middle|\frac{I}{0\dots0}\right], B= \left[C_{2}\middle|\frac{I}{0\dots0}\right]$ , where $A$ and $B$ have different first columns (represented as $C_{1}, C_{2}$). Thus we have $B = A+ \xi e_{1}^T$, where $\xi$ is a $n \times 1$ column ve...

Frenzy Li

Jul 8, 2022 06:16

@sadman-ncc His exercises are thought-provoking and tend to make you think more about linear algebra in the context of abstract algebra (e.g. groups and modules), but a strong motivation is required

Martin Sleziak

Jul 3, 2022 05:39

In any case, unless there was some mistake, we got this interesting observation: For any real square matrix, we have $\det(A^2+A+I)\ge0$.

skullpatrol

May 8, 2020 07:48

Intro: A New Way to Start Linear Algebra

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Martin Sleziak

Mar 21, 2022 07:29

$\Bbb C [x]/(2x)$ is isomorphic to $\Bbb C$, which is a field. Anyway, you can easily see that $(x+y, x-y) = (x,y)$ which is obviously a maximal ideal. — Crostul Aug 27, 2020 at 7:36

Martin Sleziak

Feb 22, 2020 11:45

3Blue1Brown's videos on linear algebra (and also other videos) are really great.

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Martin Sleziak

Sep 26, 2021 03:35

Links: doi.org/10.1080/00029890.2021.1944755 pi.math.cornell.edu/~web6720/…

Martin Sleziak

Sep 5, 2021 18:04

The applications of eigenvectors and eigenvalues | That thing you heard in Endgame has other uses

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rschwieb

Jun 7, 2021 21:17

Anyone know how to prove a corner ring of a semiperfect ring is semiperfect? This post seems to think it is true, but I don't happen to see how to do it, if it is.

BAYMAX

Mar 23, 2021 22:01

An experienced Linear & Abstract algebra chat room turned seven years recently wow!

Martin Sleziak

Feb 5, 2021 04:01

Just a reminder - to read MathJax/LaTeX in chat you can use the bookmarklet mentioned in this post on meta or go directly to robjohn's website: math.ucla.edu/~robjohn/math/mathjax.html

Simple

Oct 13, 2020 01:52

how does rounding errors affect the final results when solving matrices by row-echelon

Martin Sleziak

Sep 17, 2020 10:32

$Mathematics$ DaRT/DoME

About the Database of Ring Theory (visit ringtheory.herokuapp.com

MatheiBoulomenos

Oct 26, 2017 21:13

The correct statement is "an infinite cyclic group cannot be written as a (internal) direct product of proper subgroups"

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Martin Sleziak

Aug 21, 2020 04:35

Then you have $$(y_1,y_2,y_3,y_4)\mapsto(a_4y_2,a_1y_1,a_3y_3,a_2y_4)$$ which corresponds to the matrix $$A=\begin{pmatrix}
0 &a_1& 0 & 0 \\
a_4& 0 & 0 & 0 \\
0 & 0 & 0 &a_3\\
0 & 0 &a_2& 0 \\
\end{pmatrix}.$$

Martin Sleziak

Jul 3, 2020 18:11

BTW I found those posts by searching in SearchOnMath and ...

Martin Sleziak

Jul 3, 2020 18:11

Some general advice on searching: How to search on this site?

Manjoy Das

May 3, 2020 20:31

actually i am not able to add those links to my bookmarktab

Martin Sleziak

May 2, 2020 23:01

Just a reminder - to read MathJax/LaTeX in chat you can use the bookmarklet mentioned in this post on meta or go directly to robjohn's website: math.ucla.edu/~robjohn/math/mathjax.html

Martin Sleziak

May 2, 2020 07:50

On one hand, if $a$ is algebraic and minimal polynomial has degree $n$, then $[F(a):F]=n$, it is a finite extension.

Martin Sleziak

May 2, 2020 07:21

@ManjoyDas There are some posts on the main site which seem related: f is surjective ring homomorphism form (A,+, .) to (B, +, .) and Let $A$ and $R$ be rings and $f : A → R$ a ring homomorphism.

ms._VerkhovtsevaKatya

Apr 4, 2020 06:41

8

A: Problem book on linear algebra

My first suggestion would have been Schaum's outline. However since you have gone through that already, another book I am quite fond of (which I think covers a good portion of the topics you mentioned) is "Linear Algebra Problem Book" by Paul Halmos: http://www.amazon.co.uk/Algebra-Problem-Dolci...

BrickByBrick

Apr 3, 2020 20:44

Hey guys! I would like a recommendation about a linear algebra book. So far I have studied Terence Tao's notes on linear algebra as well as the first three chapters of Hoffman and Kunze "Linear Algebra". Based on such considerations, could someone suggest me a natural follow-up to these books which is equally reader-friendly? Thanks in advance!

Martin Sleziak

Feb 22, 2020 11:45

The determinant | Essence of linear algebra, chapter 6

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Dannyu NDos

Dec 7, 2019 01:34

Hi everyone.
I have a soft question.
The direct product operation of finite groups up to isomorphism forms a commutative monoid.
Do you think it's possible to take this as multiplicative and form a ring?
In other words, is there an additive operation on finite groups?

beerzil charlemagne

Dec 1, 2019 13:02

@MartinSleziak : On a different note , are undergrads in maths expected to complete the whole of a book like , Dummit and foote , in one semester of algebra course ?

beerzil charlemagne

Dec 1, 2019 12:14

@MartinSleziak : Do you know of any such theorem or lemma ? I was basically confused about as to why there is another theorem which is same as the first property of the euclidian ring . Then I saw the difference was the greater than and greater than or equal to sign

beerzil charlemagne

Dec 1, 2019 11:55

But then a theorem is presented stating that if $b is not a unit in R , then d(a) < d(ab) .

Is the only difference between the definition and the theorem is the greater than or equal to sign ?

Martin Sleziak

Nov 13, 2019 19:13

Well, I have only seen congruence used for square matrices, so this seems to be something different.

Eric Scöerg

Nov 13, 2019 18:37

@MartinSleziak No, sadly. A is not square, dimensionwise, lets assume it's (n×m)*(m×m)*(m×n)

Eric Scöerg

Nov 13, 2019 16:22

Hi,

can anybody tell if there is a name for $A*D*A^T$, especially D = diag(d) matrix equation?

Martin Sleziak

Sep 5, 2019 16:46

Just a reminder - to read MathJax/LaTeX in chat you can use the bookmarklet mentioned in this post on meta or go directly to robjohn's website: math.ucla.edu/~robjohn/math/mathjax.html

Kemono Chen

Aug 28, 2019 12:08

Any ideas on determining whether there is a subgroup of $\text{GL}(2,\mathbb C)$ isomorphic to $D_4\times \mathbb Z_2$?

Alex Kindel

Jul 17, 2019 02:05

A computational question: suppose you have a number field, $F$, and the minimal polynomial, $f$, of a primitive element, $x$, of $F$, so that you can represent elements of $F$ as rational polynomials in $x$ between which computations are done modulo $f$. Does taking the GCD's of polynomials whose coefficients are in $F$ using the basic Euclidean algorithm suffer from coefficient explosion?

Joshua Ronis

Jun 22, 2019 13:03

I don't think it's going to get more "geometric" than splitting it into separate component vectors in the directions that $D$ scales in (or if its a symmetric mastrix, the directions that $S$ scales in) and projecting them independently and then adding them up.

Joshua Ronis

Jun 22, 2019 13:02

@MartinSleziak I'd appreciate it so much, but honestly, don't worry about it. Look at this conversation I had on reddit:

Martin Sleziak

Jun 20, 2019 12:54

I'll just post the same linke with a slightly more readable format: A geometric question on the commutativity of inner products with symmetric matrices.

Joshua Ronis

Jun 20, 2019 12:52

Hey, I'm not sure if it's okay to request answers to questions here, but if someone has a great geometric understanding of Linear Algebra, I would REALLY appreciate an answer to this question: math.stackexchange.com/questions/3266970/…

Martin Sleziak

Jun 19, 2019 13:39

For instructions how to render MathJax(TeX) in chat see this post on meta. Or have a look at bookmarklets on robjohn's website.

Martin Sleziak

Nov 9, 2015 11:03

Just in case you do not know how to get LaTeX rendered in chat, I will add this link: math.ucla.edu/~robjohn/math/mathjax.html

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