11 consider an n k matrix a a a 11 a 12 a 1 k a 21 a

This preview shows page 2 out of 2 pages.

11. Consider an n × k matrix A : A = a 11 a 12 · · · a 1 k a 21 a 22 · · · a 2 k a 31 · · · a 3 k . . . . . . . . . . . . a n 1 a n 2 · · · a nk a ) Show that its own inner product A 0 A is symmetric. Show that their diagonal elements are given by A 0 A ii = n X j =1 a 2 ji where A 0 A ii denotes the i th diagonal element of A 0 A . b ) Show that its outer product AA 0 is also symmetric. Find their diagonal elements, and show that they can not be negative. 12. Let A and B be n × k and k × n matrices respectively. Show that tr( AB ) = tr( BA ). 13. Given the same set of matrices as in Q6, calculate the following traces of products. a ) tr( BC ) b ) tr( C 0 B 0 ) c ) tr( CB ) d ) tr[( BC ) 0 ] e ) tr( B 0 C 0 ) 2
Image of page 2
You've reached the end of this preview.

{[ 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