Help with Matrix & Operator specifics

[ognik]

Hi, those who have seen my recent posts will know that I am trying to put together a simple table that I am certain will help me get through a cloud of uncertainty that is proving a major obstacle to my on-going studies. I refer to http://mathhelpboards.com/linear-abstract-algebra-14/matrices-what-applies-what-16451.html and http://mathhelpboards.com/linear-abstract-algebra-14/matrix-amp-operator-summary-16403.html
This might be an unusual request and I hope I don't offend accidentally - but this is a disproportionate obstacle for me, and unfortunately my Prof. has declined to help.

By loose analogy, we first learn a very simplified form of mechanics - 1D Newtons laws without even vectors. That gets built on and we add vectors, rotation etc. Later we learn that the laws are a special case of the relativity version. Later on we learn that some of them don't apply in the quantum world...

Knowing how I learn best in different situations, I am trying to do something similar in a compressed timeframe. I (I don't believe it's unusual) make pages and pages of bullet points, keywords and formula as I work - I am a very visual learner. I keep coming back to them and improving them as I learn new stuff or discover inadequacies; eventually I will also have a good revision source.

So this unpopular table of mine is not an attempt to create a complete summary of Matrix and other operators, at a point in the material that am confident I can go forward from; the uncertainty around what I think I know is also clouding new material. So I just want to be sure I have everything in the right place, even if the table is otherwise unsatisfying to those with more understanding than mine. I take full responsibility for all consequences.

The idea I had last night was - would anyone be prepared to work with me 'offline' - in a private conversation, or over skype (I would not abuse such a privilege). The I can go through why I have what I have, one point at a time - and keeping it simple - my mentor can confirm what is correct and point out what is inadequate or wrong.

 

[jvicens]

Hello,

Thank you for sharing your struggle with understanding matrices and operators. It can be frustrating when we encounter obstacles in our studies, especially when we feel like we are not receiving the support we need from our professors. I commend you for taking the initiative to create a visual aid in the form of a table to help you better understand these concepts.

I would be happy to work with you offline and discuss your table in more detail. I understand the importance of having a mentor to guide and confirm your understanding. However, I do want to caution you that I am not an expert in linear abstract algebra, so I may not be able to provide all the answers you are seeking. Nonetheless, I am more than willing to help in any way I can.

In the meantime, I would suggest seeking out additional resources such as textbooks, online tutorials, or study groups to supplement your learning. Sometimes, hearing different explanations or seeing different examples can help solidify our understanding.

I wish you all the best in your studies and I am here to support you in any way I can.