problems4.2 - Math 307: Problems for section 4.2 November...

This preview shows page 1 out of 1 page.

Math 307: Problems for section 4.2November 14, 20121.(i) What can you say about the diagonal elements of a Hermition matrix?(ii) Show that ifAis ann×nmatrix such that(v,Aw)=(Av,w)thenAis Hermitian.2.Show that ifAis any matrix thenA*AandAA*are Hermitian with non-negative eigen-values.3.Follow the procedure in the notes to find an orthogonal matrixVsuch thatVTAVisupper triangular whenA=bracketleftbigg1 21 1bracketrightbigg.4.Explain why the Laplacian matrixLfor a resistor network has non-negative eigenvalues.
End of preview. Want to read the entire page?

Upload your study docs or become a

Course Hero member to access this document

Term
Fall
Professor
RICHARDFROESE
Tags
Math, Linear Algebra, Algebra, Matrices, Electrical resistance, Orthogonal matrix, Hermitian, effective resistance, non negative eigenvalues

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture