Let K be a field of characteristic zero and V a vector space over K. Then the exterior product is an associativeoperation on the alternating multilinear forms on V. In other words, if L, M, and N are alternatingmultilinear forms on V of degrees r, s, and t, respectively, then(L A M) A = L A (MA N).

Answered: Image /qna-images/answer/7cce6d71-ab64-40f2-a3dd-87b4032be656.jpg

Answered: (LA M) A = L A (MA N).

Math

Advanced Math

(LA M) A = L A (MA N).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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Question

Let K be a field of characteristic zero and V a vector space over K. Then the exterior product is an associative
operation on the alternating multilinear forms on V. In other words, if L, M, and N are alternating
multilinear forms on V of degrees r, s, and t, respectively, then
(L A M) A = L A (MA N).

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