MAT247H1 Lecture Notes - Lecture 1: Linear Map, Spanx

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23 Jan 2015
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Note: questions 1a), 2b), 3, 8 and 12e) will be marked: for each of the following inner product spaces v , let t : v v be the orthogonal projection of v on the subspace w . Suppose that h , i is an inner product on v that satis es h1, 1i = 2 h1, xi = 2 hx, xi = 4 hx, x2i = 2 h1, x2i = 2 hx2, x2i = 3. Let w = span{ x2, x}: let v = c4 with the standard inner product. W = { x = (x1, x2, x3, x4) v | 2x1 x3 = 0, x1 ix2 + x4 = 0}: let n 2, v = mn n(r), with the inner product ha, bi = trace(ab ), a, B v , and w = { a v | a = a }: let w1 and w2 be nite-dimensional subspaces of an inner product space v .

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