combinepdf-min-0221.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 17¢h October, 2016, 23:10) page 68 Now, consider the following chain of equivalent statements33: (A is upper-triangular) 4:)» (AI-J- = 0 wheneveri > j) (because this is how ”upper-triangular” is defined) 4:} (Aja = 0 whenever] >- i) (here, we have just renamed i and j as j and i) 4:)» (Aja = 0 wheneveri < j) (because j > i is equivalent to f < j) 4:} ((ATij = 0 wheneveri < j) (here, we have replaced AH by (AT) . I, because of (53)) 1,} 4:} (AT is lower-triangular) (because this is how ”lower-triangular” is defined) . Thus, Proposition 3.29 holds. D There are a few special classes of triangular matrices worth aivina names: ...
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