Multilinear mapping/Alternating/Linear subspace/Exercise
Let be a field, let and be vector spaces over , and . Show that the set of all alternating mappings (denoted by ) is a linear subspace of (where the vector space appears -fold).
Let be a field, let and be vector spaces over , and . Show that the set of all alternating mappings (denoted by ) is a linear subspace of (where the vector space appears -fold).