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.
'Dear Diary, Today I was pompous and my sister was crazy.' 'Today, we were kidnapped by hill folk never to be seen again. It was the best day ever.'
Jayne ,'Safe'
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 10:41:14 am PDT #776 of 10002
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
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.
Theodosia - Sep 25, 2005 11:39:01 am PDT #784 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'll take a raincheck.
The good news is that I've retained the cardealerphobia guy, who is like a buyer-broker for automobiles. He has a couple of likely prospects, we're going to take a test drive on Wednesday, so I could have a car by next weekend in a best case scenario situation.
Jessica - Sep 25, 2005 12:20:45 pm PDT #785 of 10002
And then Ortus came and said "It's Ortin' time" and they all Orted off into the sunset
Paul Rudnick takes on Intelligent Design: