Anyone around familiar with set theory and isomorphisms? I'd like to check a result.
Or linear algebra, for that matter? I don't remember it all that well.
All right, no one's killing folk today, on account of our very tight schedule.
Mal ,'Trash'
Natter 39 and Holding
Off-topic discussion. Wanna talk about corsets, duct tape, or physics? This is the place. Detailed discussion of any current-season TV must be whitefonted.
Emily - Sep 25, 2005 10:21:27 am PDT #774 of 10002
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
Hil R. - Sep 25, 2005 10:34:22 am PDT #775 of 10002
Sometimes I think I might just move up to Vermont, open a bookstore or a vegan restaurant. Adam Schlesinger, z''l
Emily, I'm here, for another few minutes at least.
Emily - Sep 25, 2005 10:41:14 am PDT #776 of 10002
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
Ooh! Excellent! So tell me, is phi(A)=det(A) an isomorphism from the structure (2x2 matrices, +) to the structure (Reals, +)? It seems to me like it's not one-to-one, but I did want to be sure.
I will have other questions, mwahahah.
Hil R. - Sep 25, 2005 10:44:02 am PDT #777 of 10002
Sometimes I think I might just move up to Vermont, open a bookstore or a vegan restaurant. Adam Schlesinger, z''l
So tell me, is phi(A)=det(A) an isomorphism from the structure (2x2 matrices, +) to the structure (Reals, +)? It seems to me like it's not one-to-one, but I did want to be sure.
It's not an isomorphism. You're right, it's not one-to-one; as a trivial example, any matrix where all four entries are the same will map to 0.
Ginger - Sep 25, 2005 10:50:37 am PDT #778 of 10002
"It didn't taste good. It tasted soooo horrible. It tasted like....a vodka martini." - Matilda
Lily is so beautiful. She often appears to have an air of slumming royalty, amused at the antics of the little people.
Lee - Sep 25, 2005 10:55:58 am PDT #779 of 10002
The feeling you get when your brain finally lets your heart get in its pants.
I have an odd urge to make snickerdoodles, but am too lazy to look up a recipe and figure out if I have all the ingredients.
Emily - Sep 25, 2005 11:04:07 am PDT #780 of 10002
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
Diagonal matrices are invertible, right?
Hil R. - Sep 25, 2005 11:05:08 am PDT #781 of 10002
Sometimes I think I might just move up to Vermont, open a bookstore or a vegan restaurant. Adam Schlesinger, z''l
Diagonal matrices are invertible, right?
Right.
Theodosia - Sep 25, 2005 11:27:38 am PDT #782 of 10002
'we all walk this earth feeling we are frauds. The trick is to be grateful and hope the caper doesn't end any time soon"
I need somebody to take me out to the store, yet I am too lazy to actually call anybody with a car. Besides, they might turn me down. So I may well die of hunger before long.
Lee - Sep 25, 2005 11:31:30 am PDT #783 of 10002
The feeling you get when your brain finally lets your heart get in its pants.
I'd take you, Theodosia, if I weren't dedicated to being slug like.