u/Competitive-Cut-5743

​

Hi sub,

This message is long as I tried to give as many insights as possible into my thoughts, so that for the people giving advise have ample amount of data to understand me. I'll make sure to have a TLDR; at the bottom by neglecting a few details and asking the question i wanted to. Thanks for reading. Offending anyone in any way is not my internet, I'm just providing my thoughts. I am open to conversing about them, I will gladly correct if needed.

It started about a year ago when my interests started shifting. I, 23M working as a software engineer currently. I consider myself a decent developer and I haven't come across anyone telling me I'm bad at what I do. My salary speaks for it, I got the best offer during college hiring (along with 8 other ppl from my clg ). I am from a tier 3 college and highest in tier 3 is sort of average in tier 1 college.

As pointed out, i ask questions that are relevant, propose solutions that can be used with modifications. I usually help with the big idea. With the advent of AI, I don't get the kick in my job anymore. Software engineering is on the track of becoming an accessible tool rather than a skill that is in demand. I have always felt that working in software does not actually require you to see the big picture, the tangible outcome of it. So i consider software engineering as a tool for doing what u want. In search of a big picture, doing something with purpose , I started developing an interest in finance. The motto was to become rich initially. As an engineer, who always questions "why" and is curious about things, I started questioning why in finance too. Read some articles about economics, personal finance, understood some basic concepts of financial markets, moneys, companies making money etc. Then came the urge to model all of it. That's when I started looking into maths.

I always have a special place for maths, even after staying a bit far from it. I always enjoyed getting back at math. And with my recent desire to model financial markets and kinda hatred towards my current job. I started exploring maths. So far idk if I'm in the honeymoon phase, but from not being able to understand a thing about finance, I can now follow a few low technical financial talks and contribute a bit too, asking questions seeking clarification etc.

I remember in my past when I really put in very good amount of efforts for a competitive exam ( as with anything i turned out to be above average in that too, but you don't get a lot of things if u are above avarage without significant sacrifices atleast in my target field at that time. ) I'm saying this because in the past one year, never have I felt that I have put in efforts in my current career willingly but i can think of many weekends where I sat and studied finance or math.

Another detail is although i am knowledgeable in software, i never built anything that i can proudly say. Maybe because of my lack of interest( even in college when I used to like software, i might not have seen it but it never interested me as much as maths did ) or laziness ( which i am even now currently. I wanted to finish a few math modules but didn't spend enough time to satisfy myself that I did a good amount of work let alone complete those modules. )

I am sorry for giving you my entire history, but i am in need of serious advice and in my opinion it comes from knowing a lot of details about me.

Now to the questions,

Are my thoughts valid?

Should I pursue my passion ?

Do you think I'll have enough opportunities in finance + math domain with the constraints beint graduating from a tier 3 college, no relevant formal education or experience, totally irrelevant from my current job ? If so what are they ? ( as money is also an object for me )

Would I feel the same even after a job shift or after the honeymoon phase ends, as they say grass is greener on the other side?

TLDR;

Details about me:

23M software engineer, above avarage skills, above avarage salary, above avarage in anything is what I consider myself. Does not enjoy the job anymore because it misses the big picture, lost interest and it also became very accessible ( supply high demand declining ).

Found interest in finance, always loved maths. Wanted to make a career shift to finance + maths. Still in the beginning phase, didn't do a thorough research and wanted to see if I'm thinking right.

Questions ( same as above, repeated for who are only reading TLDR section )

Are my thoughts valid?

Should I pursue my passion ?

Do you think I'll have enough opportunities in finance + math domain with the constraints beint graduating from a tier 3 college, no relevant formal education or experience, totally irrelevant from my current job ? If so what are they ? ( as money is also an object for me )

Would I feel the same even after a job shift or after the honeymoon phase ends, as they say grass is greener on the other side?

Hi sub,

This message is long as I tried to give as many insights as possible into my thoughts, so that for the people giving advise have ample amount of data to understand me. I'll make sure to have a TLDR; at the bottom by neglecting a few details and asking the question i wanted to. Thanks for reading. Offending anyone in any way is not my internet, I'm just providing my thoughts. I am open to conversing about them, I will gladly correct if needed.

It started about a year ago when my interests started shifting. I, 23M working as a software engineer currently. I consider myself a decent developer and I haven't come across anyone telling me I'm bad at what I do. My salary speaks for it, I got the best offer during college hiring (along with 8 other ppl from my clg ). I am from a tier 3 college and highest in tier 3 is sort of average in tier 1 college.

As pointed out, i ask questions that are relevant, propose solutions that can be used with modifications. I usually help with the big idea. With the advent of AI, I don't get the kick in my job anymore. Software engineering is on the track of becoming an accessible tool rather than a skill that is in demand. I have always felt that working in software does not actually require you to see the big picture, the tangible outcome of it. So i consider software engineering as a tool for doing what u want. In search of a big picture, doing something with purpose , I started developing an interest in finance. The motto was to become rich initially. As an engineer, who always questions "why" and is curious about things, I started questioning why in finance too. Read some articles about economics, personal finance, understood some basic concepts of financial markets, moneys, companies making money etc. Then came the urge to model all of it. That's when I started looking into maths.

I always have a special place for maths, even after staying a bit far from it. I always enjoyed getting back at math. And with my recent desire to model financial markets and kinda hatred towards my current job. I started exploring maths. So far idk if I'm in the honeymoon phase, but from not being able to understand a thing about finance, I can now follow a few low technical financial talks and contribute a bit too, asking questions seeking clarification etc.

I remember in my past when I really put in very good amount of efforts for a competitive exam ( as with anything i turned out to be above average in that too, but you don't get a lot of things if u are above avarage without significant sacrifices atleast in my target field at that time. ) I'm saying this because in the past one year, never have I felt that I have put in efforts in my current career willingly but i can think of many weekends where I sat and studied finance or math.

Another detail is although i am knowledgeable in software, i never built anything that i can proudly say. Maybe because of my lack of interest( even in college when I used to like software, i might not have seen it but it never interested me as much as maths did ) or laziness ( which i am even now currently. I wanted to finish a few math modules but didn't spend enough time to satisfy myself that I did a good amount of work let alone complete those modules. )

I am sorry for giving you my entire history, but i am in need of serious advice and in my opinion it comes from knowing a lot of details about me.

Now to the questions,

Are my thoughts valid?

Should I pursue my passion ?

Do you think I'll have enough opportunities in finance + math domain with the constraints beint graduating from a tier 3 college, no relevant formal education or experience, totally irrelevant from my current job ? If so what are they ? ( as money is also an object for me )

Would I feel the same even after a job shift or after the honeymoon phase ends, as they say grass is greener on the other side?

TLDR;

Details about me:

23M software engineer, above avarage skills, above avarage salary, above avarage in anything is what I consider myself. Does not enjoy the job anymore because it misses the big picture, lost interest and it also became very accessible ( supply high demand declining ).

Found interest in finance, always loved maths. Wanted to make a career shift to finance + maths. Still in the beginning phase, didn't do a thorough research and wanted to see if I'm thinking right.

Questions ( same as above, repeated for who are only reading TLDR section )

Are my thoughts valid?

Should I pursue my passion ?

Do you think I'll have enough opportunities in finance + math domain with the constraints beint graduating from a tier 3 college, no relevant formal education or experience, totally irrelevant from my current job ? If so what are they ? ( as money is also an object for me )

Would I feel the same even after a job shift or after the honeymoon phase ends, as they say grass is greener on the other side?

​

\*Type of post\*: Doubt of a concept. Not conclusion or proof.

\*Concepts\*: Linear Algebra, Rank, Projection, matrix multiplication, inverse of matrix

For the people who expect the post to be mathematically and grammatically 100 percent correct, please do read the disclaimer else please skip to the doubt section.

\Disclaimer:\* in this post, I will be loosely defining terms, i might make meaningless exceptions, but I want to know the essence or the intuition behind concepts. I lack math rigor, so if someone can edit the writing (in the comments) to make it more understandable and mathmatically readable to the community i would deeply appreciate. This post is not conclusion, it's to help me grasp the concepts by intuition. It is more of a doubt, so at any point if my assumptions or exceptions not hold then i request you to clarify them too. If intuitively ( may not be mathematically correct ) it makes sense to assume such exceptions, then please do comment on them too that such exceptions can be of use in the real world. English is not my first language, i tried my level best to phrase it in the best way possible.

Please forgive any mistakes.

Doubt:

Consider a projection, leaving the projection onto itself definition (let's forget this P\\\\\\\^2=P). We will try to calculate the essence of the projection matrix. I, in this post, to provide better visibility into my thoughts, will consider a projection that maps a 3d cube onto a 2d plane.

I will try to not talk about P\\\\\\\^2 ( which is a projection of a space parallel to the plane onto the plane ) but if you consider other points, the dimensionality is squished. Column space of the projection is one dimension lesser than the input space. Hence the matrix is not full rank. Which makes sense cause if inverse exists of a projection then P=Identity matrix.

Let us say V is my input 3xn, U is my output 2xn. ( Ideally it should be 3xn but I'm just talking about the essence. From my understanding any plane can be represented with 2d basis vectors )

P.V = U then the shape of P is 2x3, which is rectangular. But since we need to also define projections that are parallel to the plane of projection, we sort of make it a square by adding redundant values.

Can that be a possible intuitive explanation of why the projection is not full rank, (i.e. because of the so called redundant values) ?

Side doubt:

This may be a straight forward question, I want to disprove the fact talhat a projection matrix exists which translates a 2d space to a 3d space. Am I right in thinking so, if so please help me with some directions

Ps: while re reading I had another thought that my idea of any plane being represented with 2d basis can be wrong, but nevertheless decided to post to further get clarification .

​

\*Type of post\*: Doubt of a concept. Not conclusion or proof.

\*Concepts\*: Linear Algebra, Rank, Projection, matrix multiplication, inverse of matrix

For the people who expect the post to be mathematically and grammatically 100 percent correct, please do read the disclaimer else please skip to the doubt section.

\*Disclaimer:\* in this post, I will be loosely defining terms, i might make meaningless exceptions, but I want to know the essence or the intuition behind concepts. I lack math rigor, so if someone can edit the writing (in the comments) to make it more understandable and mathmatically readable to the community i would deeply appreciate. This post is not conclusion, it's to help me grasp the concepts by intuition. It is more of a doubt, so at any point if my assumptions or exceptions not hold then i request you to clarify them too. If intuitively ( may not be mathematically correct ) it makes sense to assume such exceptions, then please do comment on them too that such exceptions can be of use in the real world. English is not my first language, i tried my level best to phrase it in the best way possible.

Please forgive any mistakes.

Doubt:

Consider a projection, leaving the projection onto itself definition (let's forget this P\^2=P). We will try to calculate the essence of the projection matrix. I, in this post, to provide better visibility into my thoughts, will consider a projection that maps a 3d cube onto a 2d plane.

I will try to not talk about P\^2 ( which is a projection of a space parallel to the plane onto the plane ) but if you consider other points, the dimensionality is squished. Column space of the projection is one dimension lesser than the input space. Hence the matrix is not full rank. Which makes sense cause if inverse exists of a projection then P=Identity matrix.

Let us say V is my input 3xn, U is my output 2xn. ( Ideally it should be 3xn but I'm just talking about the essence. From my understanding any plane can be represented with 2d basis vectors )

P.V = U then the shape of P is 2x3, which is rectangular. But since we need to also define projections that are parallel to the plane of projection, we sort of make it a square by adding redundant values.

Can that be a possible intuitive explanation of why the projection is not full rank, (i.e. because of the so called redundant values) ?

Side doubt:

This may be a straight forward question, I want to disprove the fact talhat a projection matrix exists which translates a 2d space to a 3d space. Am I right in thinking so, if so please help me with some directions

Ps: while re reading I had another thought that my idea of any plane being represented with 2d basis can be wrong, but nevertheless decided to post to further get clarification .