combinepdf-min-0336.pdf - Notes on linear algebra(Monday...

This preview shows page 1 out of 1 page.

Image of page 1
You've reached the end of this preview.

Unformatted text preview: Notes on linear algebra (Monday 17th October, 2016, 23:10) page 183 TODO 3.170. Let me give three versions of the definition of det A for all a: I First version (informal and sloppy): Set ['11 £2 + + + an 51 192 . . . b” def . . _ . z] 22 1. 1. 1. Zn = sum of terms of the form :|:?1?2 - - -?m where the question marks in each term are some permutation (= rearrange- ment) of the letters a,b, . . . ,z, and the :I: sign depends on the rearrange- ment. How exactly? Any rearrangement can be sorted into increasing order (i.e., into ab . . .2) by switching pairs of letters; e.g. (for a = 5) we can sort the rearrangement caaba as follows: caebd —> cabed (here we switched 6 with b) —> bacad (here we switched c with b) —> abced (here we switched b with a) —> abca'e (here we switched a with d) . Notice that we used 4 switches here. The rule for the i Sign is: If the rearrangement needs an even number of switches. then it’s a —|—: if an odd ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern