MAT247 - Sec 6.5 - 29 - QR discussion – Conversation in Mathematics

Conversation started Feb 12, 2023 at 2:43.

leslie townes

Feb 12, 2023 02:43

dc3: why bother with any of it? everything depends on context. depending on context, matrix factorizations may be a distraction from whatever you are hoping to get from considering Ax = b. if you are solving the equation you may also care about numerical issues, or (both in numerical and non-numerical contexts) what things about A that you have already computed or had given to you, versus things about A that you do not have given and need to compute.

Ted Shifrin

QR is totally general.

Obliv

Nvm I see, $x = -y$ which when added to $x = 1 - y + (-y)$ is a solution. So the homogeneous case of any linear ODE can be added to the solution like that?

Ted Shifrin

The $Q$ has nothing to do with eigenvectors.

leslie townes

e.g. do you know that A is diagonalizable. do you have the eigenvalues or eigenvectors. [and as ted has just pointed out, the matrices "Q" in your two factorizations are generally not the same]

ペガサス Seiya

@TedShifrin there must be something wrong with me (or my brain).

Ted Shifrin

Feb 12, 2023 02:45

Obliv, a particular solution is $(1,0)$. Now add any vector on the line through the origin, yes.

Obliv

@Seiya Nothing wrong with enjoying geometry, it's the tangible visual aspect of math I really enjoy the beauty of it too

Ted Shifrin

I wasn’t saying you’re bad. I’m saying your Euclidesn geometry prowess isn’t needed for advanced geometry.

I still think geometrically, unlike leslie . :)

ペガサス Seiya

I like thinking geometrically too. Rotating and manipulating shapes in my brain. Its fun

The downside to that is sometimes I don't watch where I'm going. My eyes are open but I'm basically blind at that moment

Ted Shifrin

Did you recognize my avatar?

ペガサス Seiya

@TedShifrin you mentioned its name but I forgot. It looks like the top of a circus place or something

D.C. the III

Feb 12, 2023 02:50

@leslietownes THings for me to ponder.........it isn't lost on me that you threw in the word "context" to capture all the happenings of the day in one phrase....I see you....👀

Ted Shifrin

Obliv, you understand that they’re saying the sane thing about ODE?

@seiya It’s what you get when you rotate a common object.

Obliv

Yes, this is very deep stuff though. Not because it's any different but infinitesimals make stuff more deep

D.C. the III

@ペガサスSeiya consumed by your passion, not a bad thing. 🙂

ペガサス Seiya

@TedShifrin which common object?

Ted Shifrin

You tell me!

ペガサス Seiya

Feb 12, 2023 02:52

@D.C.theIII well true but, when you constantly walk into doors or walls then its not so fun

leslie townes

dc3: linear algebra is a particularly tricky thing to be introduced to, because some of the notions you're introduced to are fundamental to a lot of things, or the theorems you see are in some sense 'the final word' in a given setting. and then other stuff is somewhat case-specific, or involves arbitrary choices, or can be theoretically easy but computationally difficult in a way that can't be taught in an introduction. and whatever the status of these notions, they arrive all at once.

which maybe gives the impression that they're all of equal importance/applicability, and are all in simultaneous use all the time.

you could have a one-semester class entirely devoted to matrix factorizations.

Ted Shifrin

@Obliv Not really deep. It is just linear algebra in a different setting.

leslie townes

although in any given context you may not want/need to use one, or only one of a wide variety of choices has any hope of helping you.

Ted Shifrin

@leslietownes Strang endorses that!

leslie townes

he's cornered the market on that.

Conversation ended Feb 12, 2023 at 2:55.

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