#vectorspace — Public Fediverse posts

Alright, future engineers!
A **Basis** for a vector space is a minimal set of linearly independent vectors that can generate any other vector in that space.
Ex: `{[1,0], [0,1]}` is a basis for R^2.
Pro-Tip: Think of them as the fundamental 'building blocks' or coordinate axes for your space!
#LinearAlgebra #VectorSpace #STEM #StudyNotes

Alright, future engineers!
A **Basis** for a vector space is a minimal set of linearly independent vectors that can generate any other vector in that space.
Ex: `{[1,0], [0,1]}` is a basis for R^2.
Pro-Tip: Think of them as the fundamental 'building blocks' or coordinate axes for your space!
#LinearAlgebra #VectorSpace #STEM #StudyNotes

Alright, future engineers!
A **Basis** for a vector space is a minimal set of linearly independent vectors that can generate any other vector in that space.
Ex: `{[1,0], [0,1]}` is a basis for R^2.
Pro-Tip: Think of them as the fundamental 'building blocks' or coordinate axes for your space!
#LinearAlgebra #VectorSpace #STEM #StudyNotes

Alright, future engineers!
A **Basis** for a vector space is a minimal set of linearly independent vectors that can generate any other vector in that space.
Ex: `{[1,0], [0,1]}` is a basis for R^2.
Pro-Tip: Think of them as the fundamental 'building blocks' or coordinate axes for your space!
#LinearAlgebra #VectorSpace #STEM #StudyNotes

Alright, future engineers!
A **Basis** for a vector space is a minimal set of linearly independent vectors that can generate any other vector in that space.
Ex: `{[1,0], [0,1]}` is a basis for R^2.
Pro-Tip: Think of them as the fundamental 'building blocks' or coordinate axes for your space!
#LinearAlgebra #VectorSpace #STEM #StudyNotes

🚨 BREAKING: #Nerds invent yet another way to squint at squiggles and call it progress! 🚀 Apparently, mashing symbols together in "vector space" is the new black. 🙄 Remember, kids: when in doubt, slap on a fancy name and beg for donations. 💸
https://charcuterie.elastiq.ch/ #Innovation #VectorSpace #TechHumor #Fundraising #HackerNews #ngated

Alright, future engineers!

Vectors are linearly independent if no vector can be expressed as a linear combination of the others. Ex: `c1v1 + c2v2 = 0` only if `c1=c2=0`. Pro-Tip: If you can solve for any vector in terms of others, they're *dependent*! Crucial for bases.

#LinearAlgebra #VectorSpace #STEM #StudyNotes

"You can use the metric to raise an index" is what I found in one or the other physics text book. Surely I missed some context each time, so I couldn't help to swear: 🤢 , I like the indexes where they are, what is the point of raising or lowering them.

I found the answer in Gravitation, by Misner, Thorne, Wheeler but felt the need to write it down in a way I understand it best: https://miamao.de/blog/2024-06/04.Raising_or_Lowering_an_Index.html

#physics #tensor #metric #vectorspace #dotproduct #raisinganindex #mtw

"You can use the metric to raise an index" is what I found in one or the other physics text book. Surely I missed some context each time, so I couldn't help to swear: 🤢 , I like the indexes where they are, what is the point of raising or lowering them.

I found the answer in Gravitation, by Misner, Thorne, Wheeler but felt the need to write it down in a way I understand it best: https://miamao.de/blog/2024-06/04.Raising_or_Lowering_an_Index.html

#physics #tensor #metric #vectorspace #dotproduct #raisinganindex #mtw

"You can use the metric to raise an index" is what I found in one or the other physics text book. Surely I missed some context each time, so I couldn't help to swear: 🤢 , I like the indexes where they are, what is the point of raising or lowering them.

I found the answer in Gravitation, by Misner, Thorne, Wheeler but felt the need to write it down in a way I understand it best: https://miamao.de/blog/2024-06/04.Raising_or_Lowering_an_Index.html

#physics #tensor #metric #vectorspace #dotproduct #raisinganindex #mtw

"You can use the metric to raise an index" is what I found in one or the other physics text book. Surely I missed some context each time, so I couldn't help to swear: 🤢 , I like the indexes where they are, what is the point of raising or lowering them.

I found the answer in Gravitation, by Misner, Thorne, Wheeler but felt the need to write it down in a way I understand it best: https://miamao.de/blog/2024-06/04.Raising_or_Lowering_an_Index.html

#physics #tensor #metric #vectorspace #dotproduct #raisinganindex #mtw

"You can use the metric to raise an index" is what I found in one or the other physics text book. Surely I missed some context each time, so I couldn't help to swear: 🤢 , I like the indexes where they are, what is the point of raising or lowering them.

I found the answer in Gravitation, by Misner, Thorne, Wheeler but felt the need to write it down in a way I understand it best: https://miamao.de/blog/2024-06/04.Raising_or_Lowering_an_Index.html

#physics #tensor #metric #vectorspace #dotproduct #raisinganindex #mtw

Juan-Pablo Ortega form #NTU recommended a GTM by Serre. I was aware of its existence but somehow assumed that it would be harder. Maybe I'll go for that instead?

Anyway, I like in Isaacs book that it exposes what aspects of linear #vectorspace make #GroupTheory tick. Also it was really fun reading Schur-Frobenius theorem yesterday, there the #module framework came to shine. I appreciate that.

What's more trouble for me is that the notation is sometimes not introduces certain things or I'm used to \(f(x)\) as opposed to \(xf\) 🤷‍♂️. Im getting used to inline definitions made in passing but suddenly later coming into play.

I'm trying to educate myself in graduate level #mathematics and picked up this book by Isaacs on #GroupTheory characters. I managed to just so survive the first chapter which is a dense write up on #vectorspace #module theory. I'm able to read on, chapter 2 and 3 were still possible, but are there better entries into representations and characters?

Appreciate advice on:
1. easier but more specific exposition of central results?
2. advantages of developing everything in the A-module framework?
3. which chapters are key for subsequent developments?
4. which theorems are the ultimate highlights and which are 'just' key to the particular question at hand?
5. What's particularly worthwhile in the presentation approach taken in this book?

@remi Using this for multiple tags and users would turn #Mastodon into a #vectorspace (linear combination of different feeds) where you can dial in your exact position of interest. "I need to #mastoart a little to the left and #math a little more towards to Z axis"

#Meaning is usually described with #VectorSpace #Semantics as in the article below comparing the works from #CAShannon and #AMTuring:

https://www.journals.uchicago.edu/doi/full/10.1093/bjps/axx029

Basically, what vector space semantics says is that the meaning of a message depends on the #Context provided by the sender’s and the receiver’s #DynamicalSystem #Knowledge #State.

As they are two different physical entities they will obviously be in different states, so the two meaning can never be exactly the same.