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Let V be a finite-dimensional inner product space over C and let u, w V be fixed non-zero vectors such that (u, w) 0. Let T: V→ V be the linear operator defined by T(v) = (v, u)w for all v = V. 1 Find the eigenvalues and associated eigenspaces of T. 2 Explain whether T is diagonalisable.

Let V be a finite-dimensional inner product space over C and let u, w V be fixed non-zero vectors such that (u, w) 0. Let T: V→ V be the linear operator defined by T(v) = (v, u)w for all v = V. 1 Find the eigenvalues and associated eigenspaces of T. 2 Explain whether T is diagonalisable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:| W *)) +0 01:13 PM 2022-07-31 W File Paste 7,12,1,11,1,10,1,9,1,8,1,7,1,6,1.5.1,4,1,3.1.2.1,1,1,|,1,1,1.2 | | Home Page: 1 of 1 Clipboard Insert Page Layout Cut Copy Format Painter Words: 9 Calibri (Body) T BIU References 12 T Α B-B-S ## T AaBbCcDc AaBbCcDc AaBbC AaBbcc AaBI AaBb CcL 1 Normal No Spaci... Heading 1 Title Heading 2 Styles ··2·1·1·1···1·1·2·1·3·1·4·1·5·1·6·1·7·1·8·1·9·1·10 ·| · 11 · |· 12 · |· 13 · |· 14 · 1 · 15 · |-·\\ · · · 17 · · · 18. I I I I U abe X₂ X³ abe X, X² Font Α΄ A Mailings T Aa ab Aal Document1 - Microsoft Word (Product Activation Failed) View Review I Paragraph I I LINEAR ALGEBRA III Please help answer all questions below: Let V be a finite-dimensional inner product space over C and let u, w€ V be fixed non-zero vectors such that (u, w) 0. Let T: V→ V be the linear operator defined by T(v) = (v, u) w for all v € V. .1 Find the eigenvalues and associated eigenspaces of T. 2 Explain whether T is diagonalisable. Subtitle Find АА Час Replace Change Styles Select Editing G 歐美酒100% - D @? ▶O+
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