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Let V be the vector space of all n times n matrices with the inner product and W be all the n times n diagonal matrices. Show that W is a subspace of V. Let , and D = diag{lambada 1,..., lambda n) be any n times n diagonal matrix belonging to W. Show that if and only if ajj = 0 for all . Find the orthogonal complement of W in V. Show transcribed image text
All help will be rewarded
Let V be the vector space of all n times n matrices with the inner product and W be all the n times n diagonal matrices. Show that W is a subspace of V. Let , and D = diag{lambada 1,..., lambda n) be any n times n diagonal matrix belonging to W. Show that if and only if ajj = 0 for all . Find the orthogonal complement of W in V.
Show transcribed image text Keith LeannonLv2
13 Jun 2019