lecture_32 (dragged) 3

lecture_32 (dragged) 3 - i th and j columns so the...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
4 MA 36600 LECTURE NOTES: MONDAY, APRIL 13 When y k = x k σ ( k ) we use the fact that x ip = j p ij ( t ) x jp to find dW dt = σ ( σ ) d dt n k =1 x k σ ( k ) = n i =1 σ ( σ ) dx i σ ( i ) dt · k = i x k σ ( k ) = n i =1 n j =1 p ij ( t ) σ ( σ ) x j σ ( i ) · k = i x k σ ( k ) = n i =1 n j =1 p ij ( t ) · W x (1) , . . . , x ( i 1) , x ( j ) , x ( i +1) , . . . , x ( n ) ( t ) . If j = i , then the expressions above involve matrices with two equal columns (namely the
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: i th and j columns), so the determinant is zero. Hence the sum reduces to the case where j = i : dW dt = n ± i =1 p ii ( t ) W = · tr P ( t ) ¸ W....
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