Let U and V be finite-dimensional vector spaces. (a) Find a formula for dim( U V)

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Let U and V be finite-dimensional vector spaces.
(a) Find a formula for dim( U × V) in terms of dim U and dim V. (See Exercise 49 in Section 6. 1.)
(b) If W is a subspace of V, show that dim Δ = dim W, where Δ = {(w, w): w is in W}.

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Linear Algebra A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

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Question Posted: Apr 15, 2016 06:26 AM

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Let U and V be finite-dimensional vector spaces. (a) Find a formula for dim( U V)

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Let dimU m with basis B u 1 u m and dim V n with basis C v 1 v n a Claim that a basis for U V is D u ...View the full answer

Linear Algebra A Modern Introduction

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