OK, so I need to show that the set of all multilinear maps is a subspace (of, obviously, the set of all linear maps): i. e., it is closed under vector addition and scalar multiplication. I have no difficulty in showing that the set is not empty. However, I have no idea about how to show that it is closed under vector addition and scalar multiplication. I thought I could do this by simply applying the definitions and then rearranging the terms but nope. Please help!
2026-03-30 00:24:35.1774830275
Show that the set of all multilinear maps is a subspace
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