{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

take_home7

# take_home7 - 3 Wlth Initial conditions y = gm 3 = ya 3 =...

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . . . . . . 3 Wlth Initial conditions y = gm, 3% = ya, 3:!- = 93', .H, “—1 I I I if??- = 93—1, when :t: = 3:0. (Hint: convert It Into a system of first order equations and apply previous problem.) 1'3] Let R“ be equipped with the Euclidean norm llsll = [216]“ Let MHUE} be the set of rs x n. matrices. and note that MﬁR) is a rig-dimensional real vector space. Show that the formula {Ll-(A) = Ell-113-""{ll14l:-“Elll III: 1: 1} deﬁnes a norm on MAR}. Determine how to effectively compute ill-{A}- [Hints: You may use without proof the following facts from linear algebra: There is an algorithm for writing any matrix A in the form A 2 UP. where U is an orthogonal matrix and P is a symmetric matrix with nonnegative eigenvalues. Furthermore. there is an orthogonal change of basis to diagonalize a symmetric matrix.) ED] Show that the real projective plane RP“ = Smfx # —x is homeomorphic to the space of n K n symmetric matrices of rank 1. ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern