This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: (b} Show that the yz plane is not ^invariant. 7 Let T : V Â» V be a linear operator and let v â‚¬ V satisfy T(v) â€” mv where m is a fixed element of the field F. Now define the subset En = (u e V : T(u) = mil}. (a) Show that E m is a vector subspace of V. (b) Show that E m is Tinvariant. g Let L : V â€” * V be a linear Operator on the ndimcnsioim] vector space V, and let v Â£ V. (a) Let m. be the smallest integer with the property that L m (v) E Span({v,i(v) L m'(v)}. Prove that S. = Span({v, i(v),. .., L m'(v)}). C**""<ir KlÂ»u.) (b) Let L : M 2x2 fft) > A/ 2x2 (K) be given by Find a basis for the /^invariant subspace generated by 1 M oo ( l 001 1 1 1 Definition. Let L : V â€” * V be a linear operator on a vector space V and let v Â£ V. The Lcyclic subspace of V generated by v, S v , is defined by 5, = Span({v, i(v), L 2 (v) ^*( v ), â€¢â€¢ â€¢})...
View
Full
Document
This note was uploaded on 01/04/2012 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.
 Fall '08
 CELMIN
 Transformations

Click to edit the document details