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dim v=dimn Utdim W

dim v=dimn Utdim W

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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Ifvis afinite dimensional vector Space over K, and is the direct Sumof work. Subspaces U, w then proves 20 dim v=dim utdim W र
Transcribed Image Text:Ifvis afinite dimensional vector Space over K, and is the direct Sumof work. Subspaces U, w then proves 20 dim v=dim utdim W र
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Theorem: A vector space  V is the direct sum of its subspaces U and W if and only if

(i) V = U + W      (ii) U ∩ W = {0}

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