1418 remark note the characteristic polynomial is not

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: if ∃S ∈ Mn , where S is invertible, such that: B = S −1 AS This defines an equivalence relation, as can be verified. 1.4.17 Theorem. If A, B ∈ Mn are similar, then PA = PB Proof. PB (t) = det(tI − B ) = det(t(S −1 S ) − S −1 AS ) = det(S −1 (tI − A)S ) = det(S −1 )det(tI − A)det(S ) = det(S −1 S )det(tI − A) = det(tI − A) = PA (t) We conclude A, B share same eigenvalues with the same multiplicity. 1.4.18 Remark. No...
View Full Document

This note was uploaded on 01/16/2014 for the course MATH 6304 taught by Professor Bernhardbodmann during the Fall '12 term at University of Houston.

Ask a homework question - tutors are online