16. Let \( V \) and \( W \) be vector spaces such that \(\dim(V) = \dim(W)\), and let \( T: V \to W \) be linear. Show that there exist ordered bases \(\beta\) and \(\gamma\) for \( V \) and \( W \), respectively, such that \([T]^\gamma_\beta\) is a diagonal matrix.

Answer (A),Let V and W be vector spaces such that dim(V) = dim(W) and let be linear.Now, we need to…

Answered: 16. Let V and W be vector spaces such…

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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16. Let V and W be vector spaces such that dim(V) dim(W), and let T: V → W be linear. Show that there exist ordered bases ß and y for V and W, respectively, such that [T] is a diagonal matrix. =