Do i need to know all the algebra and theoretical derivations in econometrics time series (for instance, how to calculate the ACF of an AR model by hand) to be qualified to work in Quant? Or can i just know the conclusions? Thanks 

I'd think so. If you don't know how to calculate ACF or PACF you basically don't understand them. And it's not rocket science after all.
I completed this course (out of curiosity and boredom) some time ago and I think it's good: Time Series Analysis in Python Course | 365 Data Science

i see. cheers pal

As kat says, it it not rocket science but you need to know the underlying maths, not just staring at formulae but working on concrete problems by hand (a mano) until you are blue in the face and then automate the process. Time Series is applied numerical analysis, on which it builds and don't skip essential steps:

1. ODE/Numerical (e.g. J.D. Lambert 1991)
Difference operators, multistep methods, stability

2. Analytic solution of linear difference equations by characteristic polynomial roots.

2. 1,2 step AR, ARMA. ARIMA methods by hand (take a concrete example).

//
3. Discrete process, Fouier stuff.

As kat says, it it not rocket science but you need to know the underlying maths, not just staring at formulae but working on concrete problems by hand (a mano) until you are blue in the face and then automate the process. Time Series is applied numerical analysis, on which it builds and don't skip essential steps:

1. ODE/Numerical (e.g. J.D. Lambert 1991)
Difference operators, multistep methods, stability

2. Analytic solution of linear difference equations by characteristic polynomial roots.

2. 1,2 step AR, ARMA. ARIMA methods by hand (take a concrete example).

//
3. Discrete process, Fouier stuff.

Thank you so much!

You're welcome; good luck.

Meh. You definitely need to know something well, and preferably something relevant. It doesn’t have to be time series statistics, nor numerical analysis; it could be the theory and practice of term structure modeling or how to hedge equity derivatives in a rough Heston model. For a little bit of extra context, kat has not done a ton of finance quant work but can do machine learning in circles around the rest of us (and she is a pal-ette?). Cuch was around for a long time before C++ was invented, but he was an early adopter, and has forgotten more about programming than most of us ever knew. He doesn’t take well to big balls of mud or modern programming languages, though.

Meh. You definitely need to know something well, and preferably something relevant. It doesn’t have to be time series statistics, nor numerical analysis; it could be the theory and practice of term structure modeling or how to hedge equity derivatives in a rough Heston model. For a little bit of extra context, kat has not done a ton of finance quant work but can do machine learning in circles around the rest of us (and she is a pal-ette?). Cuch was around for a long time before C++ was invented, but he was an early adopter, and has forgotten more about programming than most of us ever knew. He doesn’t take well to big balls of mud or modern programming languages, though.

Touchy today, are we? If you had been a bit sharper by responding to OP w/o sniping. You gave a great answer to a question that wasn't posed. 
BTW I took a course on  TS as undergrad in 1974. It was based on difference equations.

First, OP's question was about the linear algebra foundations. Of course, thanks for educating us on the rest.

I take issues with your remarks on languages: I use C++, Python and C#. No doubt you consider Julia to be modern, I see it as dinky and cute. Have a look here.

bearish, 
Now that you ask..
FYI my C++ ODE/PDE courses are standard at Baruch, CMU, NYU, UCB..

I think you missed the memo on this new book.

viewtopic.php?t=102874

No plans for Julia or Rust, however. But a lot of Cython.

Still, I remain open to suggestions.


Rough Heston

https://www.datasim.nl/blogs/29/msc-the ... nance-2020

Re the original question, it's good to have a "high level" picture, which is supplied by this gem:
A Guide to Econometrics -- Kennedy

From the 4th edition:

Meh. You definitely need to know something well, and preferably something relevant. It doesn’t have to be time series statistics, nor numerical analysis; it could be the theory and practice of term structure modeling or how to hedge equity derivatives in a rough Heston model. For a little bit of extra context, kat has not done a ton of finance quant work but can do machine learning in circles around the rest of us (and she is a pal-ette?). Cuch was around for a long time before C++ was invented, but he was an early adopter, and has forgotten more about programming than most of us ever knew. He doesn’t take well to big balls of mud or modern programming languages, though.

Re the original question, it's good to have a "high level" picture, which is supplied by this gem:
A Guide to Econometrics -- Kennedy

From the 4th edition:
From_4th_edition20pct.jpg

I actually wanted to become an econometrician and even studied a year at an economic uni in Poland, but natural sciences turned out to be much more interesting. I have no idea why this nice word was abandoned for "quant". I remember when I first heard it from someone who got a job of a "quant" in London. I asked what it was short for - "quantum", they answered proudly. We even came up with a theory what that "quantum" meant together with my colleague at the institute of physics (quantumness referred to operating at the highest level of numerical precision achievable for computers)
Anyway, I knew people who spent over a decade working as quants and implemented one model or two. Hard to say how my experience in the field compares to that. Just as the last 3 years of my work and interest in ML doesn't define my professional background - even though I probably develop and deploy more ML models than average in the overhyped industry. Only practical experience can verify what kind of knowledge is useful. Creativity and skills are probably more crucial. I simply think it's good to enter the field with a good grasp of simple models' workings, as a reference level to the imperfect reality and heuristics (even if only to write unit tests!). But that's just my opinion.

Why is there inertia in economics for not using ODEs for time series?

https://arxiv.org/abs/1907.03907

https://arxiv.org/abs/1605.05420

I'm with kata about "practical experience". In my field (commodity trading), domain knowledge has a huge importance. So, you come with your knowledge and understanding of some models/theories, and you take bits here an there across your technical background to accomodate the intrincacies of the domain. And, working in a small team/setup, I don't seek to do beautiful things, just things that work, make sense and avoid pitfalls. LLMs? LOL Just my EoD quasi random thoughts!